Question

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

• A. 5041
• B. 11670
• C. 5040
• D. 11760

Answer 1

The Correct Option is D

To determine how many ways a committee consisting of 5 men and 6 women can be formed from a total of 8 men and 10 women, we will use combinations. The formula for combinations is given by: 

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

Firstly, let's calculate the number of ways to choose 5 men from 8 men:

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

Next, calculate the number of ways to choose 6 women from 10 women:

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

Now, the total number of ways to form the committee of 5 men and 6 women is the product of the above two combinations:

\(C(8, 5) \times C(10, 6) = 56 \times 210 = 11760\)

Therefore, the correct answer is 11760.