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
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!