Study the following information carefully to answer the questions that follows
A committee of few members to be formed out of 7 males and 5 females
In how many ways a committee can be formed of 6 members having 3 males and 3 females.

Options

A. 250
B. 300
C. 350
D. 400

Answer

To solve the problem of forming a committee of 6 members consisting of 3 males and 3 females from a group of 7 males and 5 females, we can use the combination formula, which is denoted as \( nCr \) and is calculated as:

\[ nCr = \frac{n!}{r!(n-r)!} \]

### Step-by-Step Solution:

1. **Determine the number of males and females needed:**
- We need to select 3 males from 7 males.
- We also need to select 3 females from 5 females.

2. **Calculate the combinations for males:**
- The number of ways to choose 3 males from 7 is given by \( 7C3 \).
- Using the combination formula:
\[ 7C3 = \frac{7!}{3!(7-3)!} = \frac{7!}{3! \cdot 4!} \]
- Simplifying this:
\[ 7C3 = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = \frac{210}{6} = 35 \]

3. **Calculate the combinations for females:**
- The number of ways to choose 3 females from 5 is given by \( 5C3 \).
- Using the combination formula:
\[ 5C3 = \frac{5!}{3!(5-3)!} = \frac{5!}{3! \cdot 2!} \]
- Simplifying this:
\[ 5C3 = \frac{5 \times 4}{2 \times 1} = \frac{20}{2} = 10 \]

4. **Calculate the total number of ways to form the committee:**
- Since the selections of males and females are independent, we multiply the two results:
\[ \text{Total Ways} = 7C3 \times 5C3 = 35 \times 10 = 350 \]

5. **Final Answer:**
- The total number of ways to form a committee of 6 members with 3 males and 3 females is **350**.