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Question

# Consider the letters of the word 'MATHEMATICS'. Possible number of words taking all letters at a time such that in each word both M′s are together and both T′s are together but both A′s are not together is

A
11!2!2!2!10!2!2!
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B
7!×8C2
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C
6!4!2!2!
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D
9!2!2!2!
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Solution

## The correct option is B 7!×8C2Make a group of both M′s and another group of T′s.then except A′s we have 5 letters remaining. So M′s,T′s, and the letters except A′s can be arranged in 7! ways.Therefore, total number of arrangements is 7!×8C2.

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