Suppose I have the following sequence in an event:
BABCCABAA
There are 9 elements in the sequence and I want to find the number of arrangements I get can out of this 9 elements. The order does matter but because there are repeated elements such as 4A's, 3B's, etc, it becomes not as easy as just 9 factorial. For example, the following 2 are the considered only one arrangement:
\[BA_3BCCA_4BA_1A_2\]
and
\[BA_1BCCA_4BA_2A_3\]
So how can I find the number of arrangements when there are such repeated elements in it?

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It's simple, \( \large \frac{9!}{4! \times 3! \times 2!} = 1260 \)

permutation. . i'll go with FFM

Does this come from a formula? What's the rationale behind this equation?

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