Prove Theorem $4$ by first setting up a one-to-one correspondence between permutations of $n$ objects with $n_{i}$ indistinguishable objects of type $i,\; i = 1, 2, 3,\dots, k,$ and the distributions of $n$ objects in $k$ boxes such that $n_{i}$ objects are placed in box $i,\: i = 1, 2, 3,\dots,k $ and then applying Theorem $3.$