From m-element set to n-element set: Total functions = $n^m$. Injective functions = P(n,m) = n!/(n-m)! (requires m <= n). Surjective functions = $sum_{k=0}^{n}$ (-1)^k * C(n,k) * (n-k)^m (requires m >= n). Bijective = n! (requires m = n). These counting problems are JEE favorites.