Question

In how many ways can a committee of four men and four woman be formed from a group of seven men and eleven women?

A committee of four men and four women can be formed from a group of seven men and eleven women in
different ways.
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Answer 1

Choosing 4 men from seven can be done in 7C4 = 35 ways
(There are 7 to choose from then 6 and 5 and 4 = 7 x 6 x 5 x 4
but we don’t want them in order so we need to divide by 4! = 4 x 3 x 2 x 1)
Similarly choosing 4 women from 11 can be done in 11C4 = 330 ways.

Total number of ways to choose 4 men and 4 women = 35 x 330 = 11550