Question

Compute the number of distinct arrangements of the characters ABBCCCDDDDEEEEE

Answer 1

The number of permutations of $n$  objects with $n_1$ identical objects of type 1, $n_2$ identical objects of type 2, …, and $n_k$ identical objects of type k is $\frac {n!} {n_1!n_2!...n_k!}$ . Means number of distinct arrangements is

$\frac {15!} {1!*2!*3!*4!*5!} = 37 837 800$