Toys Story

Probability Level 3

The number of ways can 14 identical toys be distributed among three boys , so that each gets at least one toy and no two boys get equal number of toys, is


The answer is 60.

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Arpit Dhimanj by Arpit Dhimanj , 23, India

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2 solutions

Rohan Jain
Jun 30, 2014

1,2,11 1,3,10 1,4,9 1,5,8 1,6,7

2,3,9 2,4,8 2,5,7

3,4,7 3,5,6

since the toys are identical each group can be formed only in 1 way, and since there are 10 groups and each group can be distributed in 3! ways so the answer comes out to be

3! x 10 = 60 qed:)

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Nisarg Dobaria
Jul 5, 2014

To divide N identical things to R groups and no group has null value The no of ways (n-1)C (r-1) So like this we get 78 now no one has same no of toys the combinations are 1 1 12, 2 2 10,...........,6 6 2 ........6 combinations And 3 types of groups of any two frndz so total combinations we have to minus is 6*3=18 So the ans is 60

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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