Circular Permutations Examples

In this class, We discuss Circular Permutations Examples.

The reader should have prior knowledge of circular permutation formulae. Click Here.

Example:

1) Take the word “hello”.

How many circular permutations are possible?

Solution:

“hello” has five characters.

Five characters are arranged in a circular in 4! ways.

We have repeated the character “l”.

So the total permutations are 4!/2!

2) The word “circular.”

Total 8 characters.

“c” repeated twice.

“a” repeated twice.

Total permutations are 7!/(2! 2!)

3) Take the characters P, Q, R, S, T, U, V, W.

P, Q, R, S are boys

T, U, V, and W are girls.

Make a circular arrangement where no two boys sit together and no two girls sit together.

Solution:

The diagram below shows the arrangement of boys.

We arrange boys in 3! ways, because circular.

The remaining four places are filled with girls in 4! ways.

Total permutations are 3! * 4!.