JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

A class contains three girls and four boys. Every Saturday, five go on a picnic (a different group of student is sent every week). During the picnic, eac 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

Correct Answer: B

Solution :

[b]

Number of girls	Number of boys	Number of groups going to picnic	Total number of dolls
1	4	\[^{3}{{C}_{1}}^{4}{{C}_{4}}\]	\[1{{(}^{3}}{{C}_{1}}^{4}{{C}_{4}})=3\]
2	3	\[^{3}{{C}_{2}}^{4}{{C}_{3}}\]	\[2{{(}^{3}}{{C}_{2}}^{4}{{C}_{3}})=24\]
3	2	\[^{3}{{C}_{3}}^{4}{{C}_{2}}\]	\[3{{(}^{3}}{{C}_{3}}^{4}{{C}_{2}})=18\]
		Total	45