The number of ways of selecting 15 teams from 15 men and 15 women

• Permutation Combination

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

Solution

For selecting the first team, number of ways of selection 1 man from 15 and 1 woman from 15 = ¹⁵C₁ × ¹⁵C₁ = 15²

Now, 14 men and 14 women are left.

For second team, number of ways of selection 1 man from 14 and 1 woman from 14 = ¹⁴C₁ × ₁₅C₁ = 14²

So, you will get a series consisting of sum of squares of first 15 natural numbers.

∑n² = n(n+1)(2n+1)/6

15² + 14² + 13² + ... + 2² + 1² = (15×16×31)/6 = 1240

The correct option is C.