Hi, So I understand this problem a little, I just can't understand the ending! So saying that we have n elements, we want all the subsets consisting of r elements where r goes from 0 to n. So we want (n choose 0) + (n choose 1) + ... + (n choose n) which is the summation of n choose r for values of r going from 0 to n. (sorry I don't know how to do the summation symbols). I'm fine so far, but then my teacher said this was equal to = summation of ( n choose r for values of r going from 0 to n ) x (1 exp r) x (1 exp(n-r)). So obviously the 1 exp r and 1 exp(n-r) will always be equal to 1. But this is where I really don't get it, she goes from this great big equation to (1+1)exp n which equals 2 exp n. Can someone please help me with this I know it's something I don't get from the summation, it's the transition I'm missing! Thank you hope the question is comprehensible!