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

Answer 1

The correct option is D $1240$

Required no. of ways $={}^{15}{C}_1.{}^{15}{C}_1+{}^{14}{C}_1.{}^{14}{C}_1+.........+{}^1{C}_1.{}^1{C}_1$

$={15}^2+{14}^2+{13}^2+.........+2^2+1^2$

$=\frac{15(15+1)(15\times 2+1)}{6}=1240$