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Lubov Fominskaja [6]
3 years ago
15

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
Mathematics
1 answer:
Readme [11.4K]3 years ago
8 0

Answer:

The number of ways is 26,400 ways

Step-by-step 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 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways  = 120 \times 220 = 26,400 \ ways

Therefore, the number of ways is 26,400 ways

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