I have trouble understanding what I'm supposed to do in some of these math questions. Here's an exam question from an old exam:
Let $A$ be a set with $n$ elements. The number of subsets of $A$ with $k$ elements is ${n \choose k}$, or: $$ C(n,k) = \frac{n!}{k!(n - k)!} $$ Show that there are as many subsets having an odd number of elements as there are subsets with an even number of elements. HINT: use the Binomial Theorem in the form: $$ (1 + x)^n = \sum_{k = 0}^n {n \choose k} x^k$$ Then set $x = -1$.
Do I just choose an arbitrary number for $n$ then set $x = -1$ and work it out? I don't know why I have such a problem understanding these questions. Thanks for your help.