Understanding Permutations with Repetitions Formulae

In this class, we discussed understanding permutations with a repetition formula.

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We take an example and understand the formulae.

Example:

Take the word COMMIT.

How many different words are possible with COMMIT?

In the word COMMIT, the character M is repeated.

If all the elements are unique, the permutations are n!

The diagram below shows different permutations of the word COMMIT.

We have two M’s. By changing the M’s, we are not getting a new permutation.

We lose an option to swap character M. for each permutation because both are the same.

So, Total permutations are divided by 2!

The formulae is N!/r!

In our example, N = 6 and r = 2.

Example:

Take the word COMMITTEE.

M repeated twice.

T repeated twice

E repeated twice.

The permutations formulae are N! /(r1! * r2! * r3!)