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Is there a general formula for the number of distinguishable arrangements of length $\ell$ of a sequence of size $s$, given the repeated elements? So,

For example, would there be a general formula to solve the problem:

How many distinguishable 5-letter arrangements are there of the word "PROBABILITY" ?

I'm looking for a general formula.

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    https://math.stackexchange.com/questions/238906/how-many-distinct-n-letter-words-can-be-formed-from-a-set-of-k-letters-where-s2017-12-09

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