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Question

Number of ways of permuting the letters of the word "ENGINEERING" so that the positions of the vowels is not changed is

A
11P5
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B
11!5!
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C
11!2!5!
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D
11P52
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Solution

The correct option is D 11P52
Total number of ways of arranging 11 things in a row is 11!
However, we have considered here the permutations of the vowels also.
From these 11 alphabets in the given word we have to keep the positions of the 5 vowels fixed.
Also, we have 3 N's and 2 G's repeated.
The required number of ways is 11!3!×2!×5!=11P52
Correct Option is D.

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