How many ways can a committee of 3 women and 2 men be formed from 6 women and 5 men?

How many ways can a committee of 3 women and 2 men be formed from 6 women and 5 men?

• A. 150
• B. 200
• C. 250
• D. 300

Answer: (B)

To determine the number of ways to form a committee of 3 women and 2 men from a group of 6 women and 5 men, we need to calculate the combinations separately for women and men and then combine the results. First, we calculate the number of ways to select 3 women from 6. This can be found using the combination formula, which is defined as: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] where \( n \) is the total number of items to choose from and \( k \) is the number of items to choose. For the women: - We need to choose 3 out of 6: \[ C(6, 3) = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20 \] Next, we calculate the number of ways to select 2 men from 5: - We need to choose 2 out of 5: \[ C(5, 2) = \frac{5!}{2!(5-2)!} =

To determine the number of ways to form a committee of 3 women and 2 men from a group of 6 women and 5 men, we need to calculate the combinations separately for women and men and then combine the results.

First, we calculate the number of ways to select 3 women from 6. This can be found using the combination formula, which is defined as:

[

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

]

where ( n ) is the total number of items to choose from and ( k ) is the number of items to choose.

For the women:

• We need to choose 3 out of 6:

[

C(6, 3) = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20

]

Next, we calculate the number of ways to select 2 men from 5:

• We need to choose 2 out of 5:

[

C(5, 2) = \frac{5!}{2!(5-2)!} =