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What fraction of seven lettered words formed using the

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What fraction of seven lettered words formed using the [#permalink]

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New post 02 Nov 2012, 13:37
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What fraction of seven lettered words formed using the letters of the words CLASSIC will have the two C's always together?

A) 2/7
B) 5/7
C) 15/19
D) 4/19
E) 2/8
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Nov 2012, 13:42, edited 1 time in total.
Renamed the topic.

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Re: What fraction of seven lettered words formed using the [#permalink]

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New post 02 Nov 2012, 13:48
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ememem wrote:
What fraction of seven lettered words formed using the letters of the words CLASSIC will have the two C's always together?

A) 2/7
B) 5/7
C) 15/19
D) 4/19
E) 2/8


The number of arrangements of CLASSIC is 7!/(2!2!) (permutations of 7 letters out of which 2 C's and 2 S's are identical).

The number of arrangements when C's are together. Consider two C's as one unit: {CC}{L}{A}{S}{S}{I}. The number of arrangements of these 6 units out of which two units (two S's are identical) is 6!/2!.

Therefore the answer is (6!/2!)/(7!/(2!2!))=2/7.

Answer: A.

Hope it's clear.

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Re: What fraction of seven lettered words formed using the   [#permalink] 02 Nov 2012, 13:48
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