A committee of 2 boys and 2 girls is to be slected from 4 boys and 3 girls . In how many ways can this be done ?

Answer

To solve the problem of selecting a committee of 2 boys and 2 girls from a group of 4 boys and 3 girls, we can break it down into steps using combinations.

### Step-by-Step Solution:

1. **Identify the Groups**: We have 4 boys and 3 girls. We need to select 2 boys from the 4 and 2 girls from the 3.

2. **Calculate the Combinations for Boys**:
- The number of ways to choose 2 boys from 4 can be calculated using the combination formula:
\[ \text{Number of ways to choose 2 boys} = \binom{4}{2} \]
- The formula for combinations is given by:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
- Applying this to our case:
\[ \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4!}{2! \cdot 2!} = \frac{4 \times 3}{2 \times 1} = 6 \]

3. **Calculate the Combinations for Girls**:
- The number of ways to choose 2 girls from 3 can be calculated similarly:
\[ \text{Number of ways to choose 2 girls} = \binom{3}{2} \]
- Using the combination formula:
\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3!}{2! \cdot 1!} = \frac{3}{1} = 3 \]

4. **Calculate the Total Combinations**:
- The total number of ways to form the committee is the product of the combinations of boys and girls:
\[ \text{Total ways} = \binom{4}{2} \times \binom{3}{2} = 6 \times 3 = 18 \]

5. **Conclusion**:
- Therefore, the total number of ways to select a committee of 2 boys and 2 girls from 4 boys and 3 girls is **18**.