<\/p>\r\n
1.\u00a0 \r\n3<\/mn>r<\/mi>+<\/mo>r<\/mi>+<\/mo>3<\/mn>=<\/mo>19<\/mn>⇒<\/mo>r<\/mi>=<\/mo>4<\/mn><\/math>\r\n<\/p>\r\n2.\u00a0 \r\nn<\/mi>=<\/mo>6<\/mn>+<\/mo>4<\/mn>=<\/mo>10<\/mn>.<\/mo> <\/mo> <\/mo> <\/mo>(<\/mo>a<\/mi>)<\/mo>120<\/mn> <\/mo> <\/mo>(<\/mo>b<\/mi>)<\/mo>66<\/mn><\/math>\r\n<\/p>\r\n3.\u00a0 \r\nk<\/mi>2<\/mn><\/msup>–<\/mo>k<\/mi>=<\/mo>2<\/mn>+<\/mo>4<\/mn>⇒<\/mo>k<\/mi>=<\/mo>3<\/mn><\/math>\r\n<\/p>\r\n4.\u00a0 \r\nC<\/mi>9<\/mn>16<\/mn><\/mmultiscripts>–<\/mo>C<\/mi>7<\/mn>16<\/mn><\/mmultiscripts>=<\/mo>0<\/mn><\/math>\r\n<\/p>\r\n5. Total-(no. beginning with1)-(beginning with21)<\/p>\r\n\r\n5<\/mn>!<\/mo>–<\/mo>4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\n6. form numbers greater than 1000<\/p>\r\n\r\n4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo><\/math>\r\n (3! , no. beginnig with 0)=18.<\/p>\r\n7.\u00a0\r\nP<\/mi>3<\/mn>6<\/mn><\/mmultiscripts>–<\/mo>P<\/mi>2<\/mn>5<\/mn><\/mmultiscripts><\/math>\r\n(no. beginning with 0)=100<\/p>\r\n8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
2.\u00a0 \r\nn<\/mi>=<\/mo>6<\/mn>+<\/mo>4<\/mn>=<\/mo>10<\/mn>.<\/mo> <\/mo> <\/mo> <\/mo>(<\/mo>a<\/mi>)<\/mo>120<\/mn> <\/mo> <\/mo>(<\/mo>b<\/mi>)<\/mo>66<\/mn><\/math>\r\n<\/p>\r\n3.\u00a0 \r\nk<\/mi>2<\/mn><\/msup>–<\/mo>k<\/mi>=<\/mo>2<\/mn>+<\/mo>4<\/mn>⇒<\/mo>k<\/mi>=<\/mo>3<\/mn><\/math>\r\n<\/p>\r\n4.\u00a0 \r\nC<\/mi>9<\/mn>16<\/mn><\/mmultiscripts>–<\/mo>C<\/mi>7<\/mn>16<\/mn><\/mmultiscripts>=<\/mo>0<\/mn><\/math>\r\n<\/p>\r\n5. Total-(no. beginning with1)-(beginning with21)<\/p>\r\n\r\n5<\/mn>!<\/mo>–<\/mo>4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\n6. form numbers greater than 1000<\/p>\r\n\r\n4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo><\/math>\r\n (3! , no. beginnig with 0)=18.<\/p>\r\n7.\u00a0\r\nP<\/mi>3<\/mn>6<\/mn><\/mmultiscripts>–<\/mo>P<\/mi>2<\/mn>5<\/mn><\/mmultiscripts><\/math>\r\n(no. beginning with 0)=100<\/p>\r\n8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
3.\u00a0 \r\nk<\/mi>2<\/mn><\/msup>–<\/mo>k<\/mi>=<\/mo>2<\/mn>+<\/mo>4<\/mn>⇒<\/mo>k<\/mi>=<\/mo>3<\/mn><\/math>\r\n<\/p>\r\n4.\u00a0 \r\nC<\/mi>9<\/mn>16<\/mn><\/mmultiscripts>–<\/mo>C<\/mi>7<\/mn>16<\/mn><\/mmultiscripts>=<\/mo>0<\/mn><\/math>\r\n<\/p>\r\n5. Total-(no. beginning with1)-(beginning with21)<\/p>\r\n\r\n5<\/mn>!<\/mo>–<\/mo>4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\n6. form numbers greater than 1000<\/p>\r\n\r\n4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo><\/math>\r\n (3! , no. beginnig with 0)=18.<\/p>\r\n7.\u00a0\r\nP<\/mi>3<\/mn>6<\/mn><\/mmultiscripts>–<\/mo>P<\/mi>2<\/mn>5<\/mn><\/mmultiscripts><\/math>\r\n(no. beginning with 0)=100<\/p>\r\n8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
4.\u00a0 \r\nC<\/mi>9<\/mn>16<\/mn><\/mmultiscripts>–<\/mo>C<\/mi>7<\/mn>16<\/mn><\/mmultiscripts>=<\/mo>0<\/mn><\/math>\r\n<\/p>\r\n5. Total-(no. beginning with1)-(beginning with21)<\/p>\r\n\r\n5<\/mn>!<\/mo>–<\/mo>4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\n6. form numbers greater than 1000<\/p>\r\n\r\n4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo><\/math>\r\n (3! , no. beginnig with 0)=18.<\/p>\r\n7.\u00a0\r\nP<\/mi>3<\/mn>6<\/mn><\/mmultiscripts>–<\/mo>P<\/mi>2<\/mn>5<\/mn><\/mmultiscripts><\/math>\r\n(no. beginning with 0)=100<\/p>\r\n8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
5. Total-(no. beginning with1)-(beginning with21)<\/p>\r\n
\r\n5<\/mn>!<\/mo>–<\/mo>4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\n6. form numbers greater than 1000<\/p>\r\n\r\n4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo><\/math>\r\n (3! , no. beginnig with 0)=18.<\/p>\r\n7.\u00a0\r\nP<\/mi>3<\/mn>6<\/mn><\/mmultiscripts>–<\/mo>P<\/mi>2<\/mn>5<\/mn><\/mmultiscripts><\/math>\r\n(no. beginning with 0)=100<\/p>\r\n8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
6. form numbers greater than 1000<\/p>\r\n
\r\n4<\/mn>!<\/mo>–<\/mo>3<\/mn>!<\/mo><\/math>\r\n (3! , no. beginnig with 0)=18.<\/p>\r\n7.\u00a0\r\nP<\/mi>3<\/mn>6<\/mn><\/mmultiscripts>–<\/mo>P<\/mi>2<\/mn>5<\/mn><\/mmultiscripts><\/math>\r\n(no. beginning with 0)=100<\/p>\r\n8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
7.\u00a0\r\nP<\/mi>3<\/mn>6<\/mn><\/mmultiscripts>–<\/mo>P<\/mi>2<\/mn>5<\/mn><\/mmultiscripts><\/math>\r\n(no. beginning with 0)=100<\/p>\r\n8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
8. 4 odd places and 4 odd nos.\u00a0\r\n×<\/mo><\/math>\r\n 3 even places (2nd, 4th, 6th)<\/p>\r\n=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
=\r\n4<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo>2<\/mn>!<\/mo><\/mrow><\/mfrac>×<\/mo>3<\/mn>!<\/mo><\/mrow>2<\/mn>!<\/mo><\/mrow><\/mfrac>=<\/mo>18<\/mn><\/math>\r\n<\/p>\r\n9. there is only 1 way in which all lamps will be switched off<\/p>\r\n10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
9. there is only 1 way in which all lamps will be switched off<\/p>\r\n
10. Two husbands can be selected out of 6 in\u00a0\r\nC<\/mi>2<\/mn>6<\/mn><\/mmultiscripts>=<\/mo>15<\/mn><\/math>\r\n ways<\/p>\r\nexcluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
excluding the wives of above 2 husbands, 2 ladies can be selected in =\r\nC<\/mi>2<\/mn>4<\/mn><\/mmultiscripts>=<\/mo>6<\/mn><\/math>\r\n ways<\/p>\r\nso, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
so, number of ways =\r\n15<\/mn>×<\/mo>6<\/mn>=<\/mo>90<\/mn><\/math>\r\n<\/p>\r\nThe above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
The above males and female can change\/choose their partner in 2 ways, so total no. of ways \r\n=<\/mo>90<\/mn>×<\/mo>2<\/mn>=<\/mo>180<\/mn><\/math>\r\n<\/p>\r\n\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u00a0<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1762","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-permutations-combinations","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1762"}],"version-history":[{"count":9,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions"}],"predecessor-version":[{"id":1791,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1762\/revisions\/1791"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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<\/p>\r\n