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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!× 8C2.
Make 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 letter except A's can be arranged in 7! ways.
Therefore, total arrangements is 7!× 8C2.

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