Total number of letters is 7 and these letters can be written in 7! ways
=7×6×5×4×3×2×1
= 5040 ways
There are seven letters in the word THERAPY including 2 vowels (E,A) and five consonants (THRPY).
Now, consider two vowels as one letter.
We have 6 letters which can be arranged in 6P6 ways = 6! ways
But vowels can be arranged in 2! ways. Hence, the number of ways that all vowels will come together = 6 ! × 2!
=1×2×3×4×5×6×2
= 1440
Total number of ways in which vowels will never come together = 5040 - 1440
= 3600