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Question

The number of different words that can be formed using all the letters of the word 'APPLICATION' such that two vowels never come together, is


A
(45)7!
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B
8!
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C
6!×7!
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D
(32)6!
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Solution

The correct option is A (45)7!
A,A,I,I,O and P,P,L,C,T,N

Let us first fix the consonants.
__     __     __     __     __     __
The consonants can be fixed in these six blank spaces in 6!2! ways.
Now, the five vowels can be placed  among seven gaps in 7C5×5!2! 2! ways.

So, total number of words =6!2!×7C5×5!2! 2!
=(45)×7!

Mathematics

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