The total number of possible teams are $^{15}C_1 \times ^{15}C_1 =225$. So the total ways of selecting $15$ teams should be $^{225}C_{15}$. I can't get where I am going wrong.
2026-03-26 03:13:28.1774494808
In how many ways can we select 15 teams from 15 men and 15 women such that each team has 1 man and 1 woman?
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1
You are going wrong because many of the teams overlap. You can't select two teams that have the same man or same woman on them. If you have two men and two women there are only two ways to form the teams because once you form the first the second is determined. Your approach would claim there are four ways.
The simple approach is to line up one sex in an arbitrary order. Now line up the other and make teams from pairs who are in the same position in the order. As there are $15!$ ways to order the second sex, there are $15!$ ways to form the teams.