In how many ways we can distribute 30 different things equally to 10 boys.

Question

In how many ways we can distribute 30 different things equally to 10 boys.

Answer 1

In how many ways we can distribute 30 different things equally to 10 boys?

 

Let's try it: first, there are 30C3 ways to distribute stuff to the first boy.

 

Then there are 27C3 ways to distribute stuff to the second boy.

 

24C3 ways to distribute stuff to boy # 3.

21C3 ways to distribute stuff to boy # 4.

18C3 ways to distribute stuff to boy # 5.

15C3 ways to distribute stuff to boy # 6.

12C3 ways to distribute stuff to boy # 7.

  9C3 ways to distribute stuff to boy # 8.

  6C3 ways to distribute stuff to boy # 9.

  3C3 ways to distribute stuff to boy #10 (this 3C3 value = 1; he simply gets what's left--no 'selectivity').

 

So the answer is the product of all of these "nC3" values.

Answer 2

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