Distribute please!

Probability Level 3

You have 20 apples and you have your 3 very best friends with you. Now you have to distribute these 20 apples among your 3 friends in such a way that none of your friend gets less than 4 apples. In how many ways can you do that?


The answer is 45.

Jai Singhal by Jai Singhal , 22, India

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1 solution

Ashwin K
Feb 23, 2016

My method for this problem : 

x + y + z = 20 //each variable takes a minimum value of 4.

We can rewrite it as, 

x' + y' + z' = 20 - 12 = 8.

The modified equation can now take whole number solution in,

10 c 2 10c_{2} ways = 10 * 9/1 * 2 = 45.

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