Fermat's Last Theorem for Binomial Coeffiecients

Let $\mathbb{N}$ denote the set of natural numbers. Then does there exist, $a,b,c,k \in\mathbb{N}$ , with $k \geq 3$ such that ${a \choose k} + {b \choose k} = { c \choose k}.$ If no solution exists write $0$ as an answer, if you think that this equation has a solution then find the value of $a + b + c + k$ .