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Permutation under Restriction

The number of...

Question

The number of ways of permuting the letters of the word DEVIL so that neither D is the first letter nor L is the last letter is:

A

36

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B

1114

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C

42

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D

73

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Solution

The correct option is D $73$
$n u m b e r o f w a y s o f a r r a n g i n g l e t t e r s o f w o r d D E V I L = 5! = 120 n u m b e r o f w a y s o f a r r a n g e m e n t w h e n D o r L a r e f i x e d = 4! + 4! - 1 = 47 ∴ r e q u i r e d p e r m u t a t i o n = 73$

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