A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority is

Step-by-step solution

A committee of 12 members is to be formed when women are in majority. Case I 9 women and 3 men aligned Number of ways = ^9 C₉ ^8 C₃ & =1 8 7 6 3 2 1 & =56 aligned Case II 8 women and 4 men Number of ways = ^9 C₈ ^8 C₄ aligned & =9 8 7 6 5 4 3 2 1 & =630 aligned Case III 7 women and 5 men Number of ways = ^9 C₇ ^8 C₅ aligned & = 9 8 2 1 8 7 6 3 2 1 & =36 56=2016 aligned aligned Required number of ways & =56+630+2016 & =2702 aligned