Combinatorics With Dolls

Probability Level 3

There are 4 girls and 3 boys in a creche. Every Saturday 5 of them are taken to picnic. The accompanying teacher gifts a doll to each girl in the picnic. After they were taken to the picnic in all possible combinations, how many dolls the girls have got altogether?


The answer is 60.

Kalpok Guha by Kalpok Guha , 21, India

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2 solutions

Bk Lim
Dec 14, 2014

Let me be the girl who is going out,

My 4 partners are selected among 6 person. 6C4=15

So I know every girl should go to picnic 15 times.

15 x 4 = 60

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Alastair Haig
Aug 25, 2014

In the group of 5 there will either be 4, 3 or 2 girls.

There are 4C4 3C1=3 combinations of 4 girls and 1 Boy, resulting in 3 4=12 dolls being gifted

Likewise, for 3 girls and 2 boys: 4C3 3C2=12 12 3=36 dolls

And for 2 girls and 1 boy 4C2 3C3=6 6 2=12 dolls

Total dolls = 12+36+12 = 60

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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