1. The problem statement, all variables and given/known data Okay so I'm trying to teach myself the first three chapters if Grimaldi before I take a discrete math course in January. I'll probably be posting a few problems. The question is as follows: In how many ways can we select n objects from a collection of size 2n that consists of n distinct and n identical objects? I found an answer key on bit torrent but I still don't understand it. It says: "For each of the n distinct objects there are two choices. If an object is not selected, then one of the n identical objects is used in the selection. This results in 2^n possible selections of size n." Could someone please illustrate this a little better for me? It's driving me nuts that I can't understand what looks like an easy problem. 2. Relevant equations Sigma(k=0,n)[ C(n,k) ] = 2^n Sigma(k=0,n)[ k ] = n(n+1)/2 C(n,r)= n!/(r!*(n-r)!) 3. The attempt at a solution Say we have n unique objects. We can change this selection by omitting one object and repeating a different one. eg. a--z, leave out 'a', but repeat 'z'. For one omission we get (n-1) different ways of doing this (b--z). For two omissions we get C(n-2,2) possibilities ... all the way up to n/2 when we run out of extra letters to double up on. This results in a sum of sorts, but not one that looks familiar. Thanks for reading!