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
• B. 45
• C. 27
• D. 24

Answer 1

Answer: (B)

45

$A$ group may consist of $1$girt, $2$ girl or $3$ girl.

(1) When there is one girl, number of groups ${=}^3{C}_1{\times }^4{C}_4=3$

(2) When there are two girls, number of groups ${=}^3{C}_2{\times }^4{C}_3=3\times 4=12$

(3) When there are three girls, number of ways $=1{\times }^4{C}_2=6$

Therefore total number of dolls $=1\times 3+2\times 12+3\times 6=45$