Division into Distinct Groups (Multinomial Coefficient)

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Number of ways to divide n distinct objects into r distinct groups of sizes $$n_1, n_2, \dots, n_r$$ (where $$n_1 + n_2 + \dots + n_r = n$$):

$$ \binom{n}{n_1, n_2, \dots, n_r} = \frac{n!}{n_1! n_2! \dots n_r!} $$
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