Multiple choice

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

  1. 980

  2. 480

  3. 470

  4. 280

  5. 1480
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total arrangements of MATRIX (6 letters) is 6! = 720. Vowels are A and I. Treating (AI) as one unit, we have 5 units (M, T, R, X, AI), which can be arranged in 5! * 2! = 240 ways. Subtracting this from 720 gives 480.

AI explanation

The word MATRIX has 6 total letters, giving 6! = 720 total possible arrangements. To use the gap method for keeping the two vowels (A and I) apart, we first arrange the 4 consonants in 4! = 24 ways, which creates 5 gaps. We then select 2 of these gaps for the vowels and arrange them in 5P2 = 20 ways, yielding 24 x 20 = 480 valid arrangements.

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