Permutations And Combinations Question 172

Question: 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

Options:

A) 21

B) 45

C) 27

D) 24

Show Answer

Answer:

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