Find one binomial coefficient equal to the following expression:
$\binom nk + 3\binom{n}{k-1} + 3\binom{n}{k-2} + \binom{n}{k-3}$
I tried to expand using the definition of $\dbinom{n}{k} = \dfrac{n!}{k!(n-k)!}$, but it was unwieldy. Which identities should I use?