Multicarrier Energy distribution & Combinatorics Problem

this problem comes out while i am thinking abt energy distribution of multicarrier system. cos each signal is linearly independent to each other, total energy is linear combination of each signal's energy. this total energy distribution is just a combinatorics problem. for a set S={a1,a2,...,a_m)has m numbers of elements. if i take out of n elements with replacement from S set and add them. i will get one value S_r where r<=m^n. so what's distinct numbers of S_r i can get? and What's numbers of occuranace for each S_r? if we know this statistics, we will be able to figure out which n (numbers of subcarrier) is the most convenience one for us to use.