Consider the letters of the word ′MATHEMATICS′.
The possible number of words that can be formed by 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
28×7!
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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 B28×7! Make one group of both M's and another group of both T's.
Arrange all of them except the A′s
The number of ways =7!
Using gap method, the total number of such words =7!××8C2=28×7!