Question

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 :

• A. 1120
• B. 1240
• C. 1880
• D. 1960

Answer 1

Answer: (B)

1240

Answer 2

Number of ways of selecting a man and a woman for a team from 15 men and 15 women
$= 15 \times 15 = (15)^2$
Number of ways of selecting a man and a woman for next team out of the remaining 14 men and 14 women.
$= 14 \times 14 = (14)^2$ Similarly for other teams
Hence required number of ways
$= \left(15\right)^{2}+\left(14\right)^{2}+....+ \left(1\right)^{2}$
$= \frac{15\times16\times31}{6} = 1240$