Question Of The Day

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?

a) 320

b) 160

c) 80

d) 200

Ans: b)160

Out of the five girls, he has to invite exactly three. This can be done in 5C3 ways. Out of the four boys, he may invite either one or two of three or four or even none of them. According to the standard formula, this may be done in (2)4 ways. Thus the total number of ways is5C3 × (2)4 = 10 × 14 = 160.