Discrete Math How many ways are there for a man to distribut

Discrete Math: How many ways are there for a man to distribute 12 indistinguishable gold coins to his 5 children if each child must recieve at least one coin?

Solution

Number of indistinguishable gold coins (n) = 12
No. of children (k)= 5

No. of ways of distributing n indistinguishable objects among k children such that each child receive at least one coin is (n-1)! / (k-1)!(n-k)! ie., 11!/4! 7! = 330 ways