Multiple choice

In how many different ways can the letters of the words EXTRA be arranged so that the vowels are never together?

  1. 120

  2. 48

  3. 168

  4. 72
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total arrangements of EXTRA = 5! = 120. Vowels are E, A. Treat (EA) as one unit: 4! * 2! = 24 * 2 = 48. Arrangements where vowels are not together = 120 - 48 = 72.

AI explanation

The word EXTRA contains 5 distinct letters, allowing for 5! total arrangements, which equals 120. The vowels are E and A; treating them as a single unit gives 4 units which can be arranged in 4! ways, and the vowels can switch places in 2! ways, yielding 48 arrangements where they are together. Subtracting the arrangements where vowels are together from the total gives 120 minus 48, resulting in 72 ways.

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