algorithms – Number of subsequence with k distinct characters

A string is a subsequence of a given string, that is generated by deleting some(possibly zero) character of a given string without changing its order.

Suppose we have string s=”aabca” and k=3. ( I will refer the three as as a1,a2 and a3 just to distinguish them).
So number of subsequence with 3 distinct characters are –

7 => (a1)bc, (a2)bc, bc(a3), (a1)(a2)bc, (a1)bc(a3), (a2)bc(a3), (a1)(a2)bc(a3)

I know how to calculate the answer for number of substring with k distinct character. How to do it for subsequence?