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!
B
8!
C
6!×7!
D
(32)6!

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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