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Question

Consider the letters of the word MATHEMATICS. Possible number of words taking all letters at a time such that at least one repeating letter is at odd position in each word is

A
11!2!2!2!9!2!2!
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B
9!2!2!2!
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C
9!2!2!
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D
11!2!2!2!
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Solution

The correct option is D 11!2!2!2!
Since there are 5 even places and 3 pairs of repeated letters, therefore at least one of these must be at an odd place. Therefore, the number of ways is 11!/(2!2!2!).

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