Question

The number of ways a committee of 3 women and 5 men can be formed from a panel of 8 men and 5 women is

• A. 940
• B. 1120
• C. 560
• D. 760
• E. 520

Answer 1

The Correct Option is C

We are given that there are 8 men and 5 women in a panel, and we are asked to find the number of ways to form a committee of 3 women and 5 men.

The number of ways to choose 3 women from 5 women can be calculated using the combination formula:

\(C(n, r) = \frac{n!}{r!(n-r)!}\) 

Where \(n\) is the total number of items, and \(r\) is the number of items to choose.

For choosing 3 women from 5, we have:

\(C(5, 3) = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10\)

Next, the number of ways to choose 5 men from 8 men is:

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

Now, to form the committee, we multiply the two values together:

\(10 \times 56 = 560\)

The number of ways to form the committee is 560.