The number of ways a committee consisting of 3 men and 1 women can be formed from 5 men and 3 women, is _____

30

The correct answer is Option (2) → 30

1. Breakdown the Selection

The committee must consist of 3 men and 1 woman. We select these from a pool of 5 men and 3 women.

• Step 1: Choose 3 men from 5

The number of ways to choose 3 men out of 5 is given by $^5C_3$:

$^5C_3 = \frac{5!}{3!(5-3)!} = \frac{5 \times 4 \times 3}{3 \times 2 \times 1} = 10$

• Step 2: Choose 1 woman from 3

The number of ways to choose 1 woman out of 3 is given by $^3C_1$:

$^3C_1 = \frac{3!}{1!(3-1)!} = \frac{3}{1} = 3$

2. Calculate Total Ways

Since the selection of men and women are independent events, we multiply the number of ways together:

$\text{Total Ways} = 10 \times 3 = 30$

Conclusion: There are 30 different ways to form the committee.