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Question

Consider the letters of the word MATHEMATICS. There are eleven letters some of them are identical. Letters are classified as repeating and non-repeating letters. Set of repeating letters{M,A,T}. Set of Possible number of words taking all letters at a time such that atleast one repeating letter is at odd position in each word, is?

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

The correct option is B 11!2!2!2!
The total no. of letters in the word is 11
They can be arrange in 11! ways
Here they are 3 identicals letters
The are repeated 2 times each So the no .of ways is 11!2!2!2!

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