Question

A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of exactly 3 women?

Answer 1

Number of men = 8

Number of women = 4

Number of peoples in the committee = 7

Exactly 3 women

In a 7 member committee, women must be 3. Therefore, the remaining 4 must be men.

The number of ways of selecting 3 women from 4 women = 4C₃

The number of ways of selecting 4 men from 8 men = 8C₄

∴ The total number of ways of selection is = 4C₃ × 8C₄ 

= `(4!)/(3!(4 - 3)!) xx (8!)/(4!(8 - 4)!)`

= `(4!)/(3! xx 1!)xx (8)/(4! xx 4!)`

= `(4 xx 3!)/(3!) xx (8 xx 7 xx 6 xx 5 xx 4!)/(4! xx 4!)`

= `4 xx (8 xx 7 xx 6 xx 5)/(4!)`

= `(4 xx 8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1)`

= 8 × 7 × 5

= 280