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Q.
A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to
be exactly three girls in the invitees?
Permutations and Combinations
Solution:
Out of 5 girls, he has to invite exactly three. This can be done in ${ }^5 C _3$ ways. Out of the 4 boys, he may invite either one or two or three or four or even none of them. This may be done in $(2)^4$ ways. Thus the total number of ways is ${ }^5 C _3 \times(2)^4=10 \times 16=160$