How many words can be made using all the letters of FACETIOU

How many words can be made using all the letters of FACETIOUSLY if the requirement is that “a” and “ e” must be together, “i” and “o” must be together, and “u” and “y” must be together.

Solution

total no. of alphabets in the word facetiously = 11

we have to 3 pair of two alphabets that equals 6

remaining= 5

now,

now consider a pair of alphabet as one.so, the no. of positions to work on will be 5+ 3 pairs= 5+3=8

now 8 alphabets can be arranged in 8! ways and each pair as 2!.as we have 3 pairs the end result would be

8!*2!*2!*2!= 322560

ans- 322560 words can be formed by using the above conditions