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. $15!$
• C. $\left(15 !\right)^{2}$
• D. $14!$

Answer 1

The Correct Option is B

First team can be selected in $\left( \, ^{15} C_{1} . ^{15} C_{1}\right)$ way second in $\left(^{14} C_{1}\right)\left(^{14} C_{1}\right)$ way's and so on So number of ways of selections $15$ teams $=\frac{\left(15 !\right)^{2}}{15 !}=\left(15 !\right)$