Proposition: Multinomial Coefficient

Assume, there are \(n\) objects of \(m\) different types. Assume, in addition, there are exactly \(k_i\) indistinguishable objects of each type, i.e. \(k_1+k_2+\ldots+k_m=n.\) Then the number of possible and distinguishable arrangements of the \(n\) objects is given by the multinomial coefficient

\[\binom n{k_1,k_2,\ldots,k_m}:=\frac{n !}{k_1 !k_2 !\cdot\ldots \cdot k_m !}.\]

Proofs: 1 Examples: 1

  1. Theorem: Multinomial Theorem

Parts: 1
Proofs: 2 3
Theorems: 4

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  1. Matoušek, J; Nešetşil, J: "Invitation to Discrete Mathematics", Oxford University Press, 1998