Question

Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women

Answer 1

The number of ways is 26,400 ways

Explanation:

Given;

total number of men, M = 10

total number of women, W = 12

number of committees to be formed = 6

If there must be equal gender, then it must consist of 3 men and 3 women.

`The \ number \ of \ ways = 10C_3 * 12C_3\\\\The \ number \ of \ ways =(10!)/(3!7!) * (12!)/(3!9!) \\\\T he \ number \ of \ ways = 120 * 220 = 26,400 \ ways`

Therefore, the number of ways is 26,400 ways