Permutations and Combinations
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.