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Question

Number of different words that can be formed from the word 'PERMUTATIONS' such that there should be atleast two alphabets between 'M' and 'A' are

A
11!10!
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B
90×10!
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C
54×10!
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D
45×10!
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Solution

The correct option is D 45×10!

Required number of words = total words - total words having less than two alphabets between 'M' and 'A'
Total words=12!2!
Total words having less than two alphabets between 'M' and 'A=Total words having no alphabets between 'M' and 'A+ Total words having one alphabet between 'M' and 'A

Total words having no alphabets between 'M' and 'A =11!2!×2!
Total words having one alphabet between 'M' and 'A =8×10!2!×2! when T is not in between+10!×2! when T is in between


Total numbers = 11!2!×2!+8×10!2!×2!+10!×2!
Required number of words=12!2!(11!2!×2!+8×10!2!×2!+10!×2!)
=45×10!


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