A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls ?
(ii) atleast 3 girls ?
(iii) atmost 3 girls ?

Explanation

To solve the problem of forming a committee of 7 members from 9 boys and 4 girls, we will break down the solution into three parts according to the conditions given in the question.

### (i) Exactly 3 girls

1. **Choose 3 girls from 4**: We need to select exactly 3 girls from the available 4 girls. The number of ways to do this is given by the combination formula \( C(n, r) \), which is calculated as:
\[ C(4, 3) = \frac{4!}{3!(4-3)!} = \frac{4!}{3! \cdot 1!} = 4 \]
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