Answer & Explanation
Given word is THERAPY.
Number of letters in the given word = 7
These 7 letters can be arranged in 7! ways.
Number of vowels in the given word = 2 (E, A)
The number of ways of arrangement in which vowels come together is 6! x 2! ways
Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.