Four couples (husband and wife) decide to form a committee of four members. 

The number of different committees that can be formed in which no couple finds a place, is

A committee may consists of all men and no women or all women and no men or 3 men and 1 women whose is not among wives of 3 chosen men or, 2 men and 2 women who are not among the wives of 2 chosen men or 1 men and 3 women none of whom is wife of chosen men.

$\therefore$ Required number of committees

${=}^4{C}_4{+}^4{C}_4{+}^4{C}_3{\times }^1{C}_1{+}^4{C}_2{\times }^2{C}_2{+}^4{C}_1{\times }^3{C}_3=16$