The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :

(1) 1880 (2) 1120 (3) 1240 (4) 1960

Dear Student,
Please find below the solution to the asked query:

As, each 15 teams selected should consists a man and a woman.So, 1st team can be selected in C115×C115 ways i.e. 152 ways      As, one man and one woman is selected from each group2nd team can be selected in C114×C114 ways i.e. 142 ways          As, one man and one woman is selected from remaining members of the respective group3rd team can be selected in C113×C113 ways i.e. 132 ways...15th team can be selected in 12 waysSo, the total numbers of ways of selecting 15 teams=152+142+132+...+12=15×16×316       As, sum of square of first n terms i.e. Σn2=nn+12n+16=1240Hence, the correct option is 3.

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  • 2
It says each team must have one man and one woman
There are 15 men and 15 women and the first team of can be selected in 15 ways
Because for every 1 man in men team any of the 15 women can be selected
Same way, the second team can be selected in 14 ways
Because the number is only 14 for both men and women
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