Compute the number of distinct arrangements of the characters ABBCCCDDDDEEEEE

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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

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

Compute the number of distinct arrangements of the characters ABBCCCDDDDEEEEE

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Question ID: mtid-5-stid-8-sqid-3575-qpid-2274