Question

Four couples (husband and wife) decido to form a committee of four members. The number of different committees that can be formed in which no couple finds a place Is

Answer 1

There are four couples such that there are four men and four women.

$\therefore$ The number of committees of $4$ men$={}^4{C}_4=1$

The number of committees of $3$ men and $1$ women$={}^4{C}_3{}^1{C}_1=4$

The number of committees of $2$ men and $2$ women$={}^4{C}_2{}^2{C}_2=6$

The number of committees of $1$ men and $3$ women$={}^4{C}_1{}^3{C}_3=4$

The number of committees of $4$ women$={}^4{C}_4=1$

$\therefore$ The number of different committees that can be formed in which no couple finds a place$=1+4+6+4+1$

$=16$.