please help solving this combinatorics problem

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problem link

for those who dont know

this is a easy problem based on permutations and combinations

the number of ways of selecting n marbles , such that each marbles of atleast 1 type is selected considering k types is same as

(number of ways of getting sum n of k numbers and each number is greater than equal to 1 )

it is same as finding the coefficient of x^n in binomial expansion of

(x+x^2+x^3+x^4…)^k

this comes out to be C(n-1,k-1)