Permutations with Repetitions Examples on Alphabets1

In this class, We discuss Permutations with Repetitions Examples on Alphabets1.

The reader should have prior knowledge of permutations with repetitions formulae. Click Here.

Example:

mississippi

1) Total words possible with the word mississippi.

Total characters: 11.

s repeated four times

i repeated four times.

p repeated two times.

From the formulae of repetitions, we write 11!/(4! 4! 2!)

2) Total words start with p.

The first position should be filled with p

The remaining ten positions should be filled with ten characters.

One p is used in the first position. So, we use the second p in the ten characters.

The total permutations are 10! / (4! 4!)

3) Start with p and end with i.

The first and last positions are filled with p and i.

The remaining characters are filled in between.

Total = 9! /(4! 3!)

4) Vowels together and consonants together.

The vowel present is i.

iiii should be considered an element.

Consonants are msssspp.

msssspp should be together.

The elements iiii and msssspp can be arranged in 2! ways.

Inside the msssspp we can rearrange.

msssspp can be arranged in 7!/(4! 2!)

Total = 2! * 7!/(4! 2!).