Binomial probability ($\mathbb{P}(X=k)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)p^k(1-p{)}^{n-k}$)

The binomial distribution with parameters $n$ and $p$ assigns the displayed probability to $k$ successes, for integers $0\le k\le n$. Each specified sequence of independent trials has probability $p^k(1-p{)}^{n-k}$, and the binomial coefficient counts the sequences with exactly $k$ successes. Outside this range the probability is zero.