In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together?

Number of ways of arranging seven letters = 7! 
Let us consider the two vowels as a group 
Now the remaining five letters and the group of two vowels = 6
These six letters can be arranged in 6!2! ways( 2! is the number of ways the two vowels can be arranged among themselves)
The number of ways of arranging seven letters such that no two vowels come together
= Number of ways of arranging seven letters - Number of ways of arranging the letters with the two vowels being together
= 7! - (6!2!)
= 3600