A committee of 5 is to be formed from a group of 12 students consisting of 8 boys and 4 girls in how many ways can the committee be formed it
consists of exactly 3 boys and 2 girls ,

Answer

To solve the problem of forming a committee of 5 members consisting of exactly 3 boys and 2 girls from a group of 12 students (8 boys and 4 girls), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Groups**: We have a total of 12 students, which includes 8 boys and 4 girls.

2. **Determine the Selection Requirements**: We need to select 3 boys and 2 girls for the committee.

3. **Calculate the Number of Ways to Select Boys**:
- The number of ways to choose 3 boys from 8 can be calculated using the combination formula \( nCr \), which is given by:
\[ nCr = \frac{n!}{r!(n-r)!} \]
- For our case, this becomes:
\[ 8C3 = \frac{8!}{3!(8-3)!} = \frac{8!}{3!5!} \]
- Simplifying this:
\[ 8C3 = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = 56 \]

4. **Calculate the Number of Ways to Select Girls**:
- The number of ways to choose 2 girls from 4 is also calculated using the combination formula:
\[ 4C2 = \frac{4!}{2!(4-2)!} = \frac{4!}{2!2!} \]
- Simplifying this:
\[ 4C2 = \frac{4 \times 3}{2 \times 1} = \frac{12}{2} = 6 \]

5. **Calculate the Total Number of Ways to Form the Committee**:
- The total number of ways to form the committee is the product of the number of ways to select boys and girls:
\[ \text{Total Ways} = 8C3 \times 4C2 = 56 \times 6 = 336 \]

### Final Answer:
The total number of ways to form the committee of 5 members consisting of exactly 3 boys and 2 girls is **336**.

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