In how many ways we can pick K elements from set of n elements to form a number X?

Question

There is one important point - We can pick any element any number of times but the total picked element should be equal to K.

For example - If set of elements is 1 2 3 5 and K = 3 and X = 4.

Then answer is 1 because there is only one way to pick 3 elements which adds upto 4 and those 3 elements are two 1's and one 2. (1+1+2 = 4)

An algorithm can greatly help. :)

Answer 1

Let's consider DP solution for coin change problem. Usually entries of array A with length (Sum+1) contain integers - number of ways to make the value of every cell.

Simple modification - make 2D array A[Sum+1][K], so A[M][P] will contain number of ways to make value M using P coins.