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Q.

The number of ways in which the letters of the word ‘SUCCESSFUL’ be arranged such that no two S’s will come together is

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a

7!2!2!

b

7!2!2! 8P33!

c

7!2!2!8P3

d

P3   8

answer is D.

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Detailed Solution

SUCCESSFUL – 10 letters [3 S’s, 2 U’s, 2 C’s, 1 E, 1 F, 1 L]

First arrange U, C, C, E, F, U, L in 7!2!2! ways

In these letters we have 8 gaps between them

In 8 gaps 3 S’s can be arranged in  8P33! ways

No two S’s come together

 8P33!×7!2!2!.

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The number of ways in which the letters of the word ‘SUCCESSFUL’ be arranged such that no two S’s will come together is