A committee of 7 has to be formed from 9 boys and 4 girls. In how | Filo
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Class 11

Math

Algebra

Permutations and Combinations

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A committee of has to be formed from boys and girls. In how many ways can this be done when the committee consists of:
(i) exactly girls?
(ii) at least girls?
(iii) at most girls?

Solution: (i) exactly girls 

This means you have to choose girls from and boys from to form a committee of . This can be done in 

(ii) At least girls 

This means girls can either be or  
So first choose girls and boys or girls and boys 
Total ways = +

(iii) At most girls 

This means we have to choose or or girls 
So this can be done in 
+ + ways.
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