Given a simple random graph $G$ with $n$ vertices where every edge is present with probability $p$ independently of the others, what is the probability that $G$ contains a clique of size $m$?
The probability that a particular set of $m$ vertices is a clique is $p^{m \choose 2}$ and there are ${n \choose m}$ such sets, but the probability clearly isn't ${n \choose m}p^{m \choose 2}$...so what do I do?