In ZFC without Replacement, the number of functions from an $N$-element set to an $M$-element set is $M \times (M - 1) \times \ldots \times (M - (N - 1))$.

In ZFC without Replacement, the number of functions from an $N$-element set to an $M$-element set is $M \times (M - 1) \times \ldots \times (M - (N - 1))$.