How many pairs of parallel edges, such as $\overline{AB}$ and $\overline{GH}$ or $\overline{EH}$ and $\overline{FG}$, does a cube have?
A word is an ordered, non-empty sequence of letters, such as word or wrod. How many distinct words can be made from a subset of the letters $\textit{c, o, m, b, o}$, where each letter in the list is used no more than the number of times it appears?
Show that the following relation holds for any positive integers $1 < k \le m < n$: $$\binom{n}{k}m^k > \binom{m}{k}n^k$$
Let $m$ and $n$ be positive integers satisfying $1 < m < n$. Show that $(1+m)^n > (1+n)^m$.