Multiple choice

In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together?

  1. 12

  2. 18

  3. 30

  4. 36

  5. 72
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D Correct answer
AI explanation

The word MAXIMA has three vowels (A, A, I) that must stay together, so we treat them as a single object. The remaining three consonants (M, X, M) along with this vowel block give 4 objects to arrange, but since M repeats twice, there are 4! / 2! arrangements. Within the vowel block, the letters can be arranged in 3! / 2! ways because A repeats twice. The total number of arrangements is (4! / 2!) multiplied by (3! / 2!), which equals 12 times 3, or 36. The result is 36.

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