Probability & Combinatorics
Intermediate

Permutations of a Multiset

Arrangements of n items where some are identical.

Formula

n!n1!n2!⋯nk!\frac{n!}{n_1! n_2! \cdots n_k!}

Variables

nTotal items
n_iCount of each identical group

Example

MISSISSIPPI: 11!/(4!4!2!) = 34650

Did You Know?

Repeated letters reduce the number of distinct arrangements.

countingarrangement