## Arrangement of letters of word “ALLAHABAD”

Question

In how many ways the vowels of the word ALLAHABAD will occupy the even places

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Utkarsh Gupta likes this.

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Mathematics
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## Answer ( 1 )

Hi Rahul

ALLAHABAD = 9 letters

Out of these 9 letters, there is 4 A’s and 2 L’s are there.

So, permutations =

9!/(4!.2!)= 7560.

There are 4 vowels and all are alike 4A’s.

_2 _4_6_8_

These even places can be occupied by 4 vowels. In 4!/4! = 1 Way.

In remaining five places 5 other letter can be occupied of which two are alike, 2L’s.

The number of ways = 5!/2! Ways.

Hence, the total number of ways in which vowels occupy the even places = 5!/2! *1 = 60 ways.

Let me know if you need any further explanation. Thanks. Happy Learning!

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