PermutationsA with repetition

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Returns the number of permutations with repetition for a given number of objects.

syntax

PermutationsA(number_all_objects [; repeat_object1; repeat_object2;...])

returns

integer number >= 0

info

- given numbers are convert into integer numbers

- number_all_objects must be greater or equal than sum of all objects repetitions

Formula of the function: n!/(k₁!*k₂!*...*k_n!)

example

PermutationsA(18;5;3;4) = 370507737600

example 2

How much different words (sense is not required) can we create using all letters of word "mathematics".

Word "mathematics" has 11 letters (that is number_objects=11).

Repetitions of letters:

- letter "m" -  repeats itself 2 times (mathematics) repeat_object1=2

- letter "a" -  repeats itself 2 times (mathematics) repeat_object2=2

- letter "t" -  repeats itself 2 times (mathematics) repeat_object3=2

Other letters are not repeat itself.

solution

PermutationsA(11;2;2;2) = 4989600

answer

We can create 4989600 different words.

notice

• If none of letters are not repeat (e.g. "home") use function Permutations