Multiple choice

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

  1. 1200

  2. 3600

  3. 2400

  4. 3200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total arrangements of THERAPY (7 letters, 2 vowels E, A) is 7! = 5040. Treat (EA) as one unit, arrangements = 6! * 2! = 1440. Vowels never together = 5040 - 1440 = 3600.

AI explanation

The word THERAPY has 7 distinct letters with 2 vowels (E and A), so the total number of unrestricted arrangements is 7 factorial. To find the arrangements where the vowels never come together, we first calculate the arrangements where they are together by treating the vowels as a single unit, giving 6 factorial multiplied by 2 factorial for their internal arrangement, which equals 1440. Subtracting the arrangements where vowels are together from the total gives 5040 minus 1440, resulting in 3600.

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