A committee of 5 people is to be chosen from a group of 6 men and 4 women. How many committees are possible if there is to be a majority of women?

A committee of 5 people is to be chosen from a group of 6 men and 4 women. How many committees are possible if there is to be a majority of women?

Answer Details

If the majority are women implies that:

3 Women and 2 Men Or 4 Women and 1 Man

= 4C3×6C2+4C4×6C1 ${}^{\mathrm{<br>}}$

= 4×15+1×6 $4\times 15+1\times 6$

= 60 + 6 = 66