In how many ways can we select n objects from a collection of size 2n that consists of n distinct and n identical objects? In how many ways can we select $n$ objects from a collection of size $2n$ that consists of $n$ distinct and $n$ identical objects?
The answer is $2^n$ and I really don't see how they get this. Selecting $n$ distinct from $2n$ is $\binom{2n}{n}$.

Note that the set of objects chosen is determined by which of the distinct objects are chosen and how many of the identical objects are chosen.  For each of the $2^n$ subsets of the $n$ distinct objects, the number of identical objects we need to take in order to fill our quota of $n$ total objects is uniquely determined.  Hence there are $2^n$ total ways to take $n$ total objects from $n$ distinct and $n$ identical objects.
