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Question

A class contains three girls and four boys. Every Saturday, five go on a picnic (a different group of students is sent every week). During the picnic, each girl in the group is given a doll by the accompanying teacher. If all possible groups of five have gone for picnic once, the total number of dolls that the girls have got is

A
21
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B
45
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C
27
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D
24
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Solution

The correct option is C 45
A group may consist of 1girt, 2 girl or 3 girl.
(1) When there is one girl, number of groups =3C1×4C4=3

(2) When there are two girls, number of groups =3C2×4C3=3×4=12

(3) When there are three girls, number of ways =1×4C2=6

Therefore total number of dolls =1×3+2×12+3×6=45

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