Question

In how many ways can a committee of 7 members be selected from 6 men and 5 women consisting of 4 men and 3 women ?

• A. 25
• B. 147
• C. 150
• D. 600

Answer 1

The Correct Option is C

To solve the problem of selecting a committee consisting of 4 men and 3 women out of 6 men and 5 women, we use combinations since the order of selection does not matter. The combination formula is given by: \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \)

First, calculate the number of ways to select 4 men from 6 men:

\( \binom{6}{4} = \frac{6!}{4!(6-4)!} = \frac{6 \times 5}{2 \times 1} = 15 \)

Next, calculate the number of ways to select 3 women from 5 women:

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

The total number of ways to form the committee is the product of the two combinations:

\( \binom{6}{4} \times \binom{5}{3} = 15 \times 10 = 150 \)

Hence, there are 150 ways to select 4 men and 3 women to form the committee.