Question

A club with five men and six women wish to form a committee. The number of men must be between 1 and 3 (inclusive), and the number of women must be between 2 and 4 (inclusive). How many different committees can be formed?

Answer 1

1250 different committees can be formed

Explanation:

We are told that the club has 5 men and 6 women.

Now we want to choose number of men between 1 and 3 with both inclusive and number of women between 2 and 4 with both inclusive.

We'll use the combination formula;

C(n, r) = n! / [r! (n - r)!]

Where, n = population and r = picks

Thus, we'll multiply the results of the women and men together. And so we have:this gives us ;

(5C1 + 5C2 + 5C3) * (6C2 + 6C3 + 6C4) = (5 + 10 + 10) * (15 + 20 + 15) = 25 * 50 = 1250 ways