Erdős Problem #386 — Let $2\leq k\leq n-2$. Can $\binom{n}{k}$ be the product of consecutive primes infinitely often?

Let $2\leq k\leq n-2$. Can $\binom{n}{k}$ be the product of consecutive primes infinitely often? For example $\binom{21}{2}=2\cdot 3\cdot 5\cdot 7.$