# 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:At Most 3 Girls? - Mathematics

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:at most 3 girls?

#### Solution

A committee of 7 has to be formed from 9 boys and 4 girls.

When the committee consists of at most 3 girls:

Required number of ways =${}^4 C_0 \times^9 C_7 + {}^4 C_1 \times^9 C_6 + {}^4 C_2 \times^9 C_5 +^4 C_3 \times^9 C_4 = 36 + 336 + 756 + 504 = 1632$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 30.3 | Page 17

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