Permutations with Repetition

Permutations with Repetition

How to solve permutation with repetition problems: example and its solution.

Example

By using numbers {4, 4, 4, 5, 5, 6, 6} once, how many 7-digit numbers can be made?

There are 3 of '4', 2 of '5', and 2 of '6'.

There are 7 numbers and you select 7 in order.

So this is a permutation with repetition problem.

Then the answer is 7!/(3!⋅2!⋅2!).