Question

A class contains three girls and four boys. Every Saturday, a group of $5$ students 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

The correct option is B $45$

$\begin{array}{cccc}\text{Number}& \text{Number}& \text{Number of}& \text{Number}\\ \text{of girls}& \text{of boys}& \text{groups going}& \text{of dolls}\\ & & \text{to picnic}& \\ 1& 4& {}^3{C}_1{}^4{C}_4=3& 1\times 3=3\\ 2& 3& {}^3{C}_2{}^4{C}_3=12& 2\times 12=24\\ 3& 2& {}^3{C}_3{}^4{C}_2=6& 3\times 6=18\end{array}$

Total number of dolls $=3+24+18=45$