A class contains 3 girls and four boys. Every Saturday five students go on a picnic, a different group of students is being sent each week. During the picnic, each girl in the group is given a doll by the accompanying teacher. All possible groups of five have gone once, the total number of dolls the girls have got is:
(A) 21 (B) 45
(C) 27 (D) 24
865Answer should be (B).
Total no. of picnics is 21. Out of them, only one girl goes in 3C1 X 4C4=3 ways. Thus 3 dolls are given.
Exactly 2 girls go in 3C2 X 4C3=12 ways. Thus 12 X 2=24 dolls are given.
Exactly 3 girls go in 3C3 X 4C2=6 ways. Thus 6 X 3=18 dolls are given.
Total no. of dolls given is 3+24+18=45.
10577C5=21.
Ketan Chandak sorry..i found out the no of picnics...the rest is written below.. :P
66I have approached the question in a different way:
1st let us fix one girl and find out how many dolls she could get
Case 1: She goes with 2 girls and 2 boys and that can happen in 4C2 ways i.e. 6 ways
Case 2: She goes with 1 girl and 3 boys and that can happen in 2C1*4C3 i.e. 8 ways
Case 3: She goes with 4 boys and that can happen in 1 way only.
Hence the no of possible ways in which she can go/get a doll = 6+8+1 = 15.
As there are 3 girls in the group, the total no. of dolls the girls have got is 15*3 = 45
