In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

General
1

in how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

2

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

To determine the number of ways a committee can be formed with 5 men and 6 women from a pool of 8 men and 10 women, we can use the combination formula. The number of ways to choose r items from a set of n items is given by the combination formula:

C(n, r) = \frac{n!}{r!(n-r)!}

Where:

  • n is the total number of items
  • r is the number of items to be chosen
  • ! denotes factorial, which is the product of all positive integers up to that number

First, let’s find the number of ways to choose 5 men from 8 men and 6 women from 10 women:

C(8, 5) = \frac{8!}{5!(8-5)!} = \frac{8!}{5!3!} = \frac{8*7*6}{3*2*1} = 56

C(10, 6) = \frac{10!}{6!(10-6)!} = \frac{10!}{6!4!} = \frac{10*9*8*7}{4*3*2*1} = 210

Now, to find the total number of ways to form a committee consisting of 5 men and 6 women, we multiply the number of ways to choose men and women:

56 * 210 = 11760

Therefore, a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women in 11760 different ways.