A class contains three girls and four boys. Every Saturday five students go on a picnic, a different group being sent each week. During the picnic, each girl in the group is given a doll by the accompanying teacher. After all possible groups of five have gone once, the total number of dolls the girls have got is
a) 27
b) 11
c) 21
d) 45
Ans: d)45
Number of groups having one girl = 3C1 ×4C4 = 3; Number of groups having two girl = 3C2 ×4C3 = 12; Number of groups having three girl = 3C3 ×4C2 = 6 ∴ total number of dolls = 3 5 1 + 12 × 2 + 6 5 3 = 45.
