Multiple choice

Consider the word 'QUESTION': How many 8-letter words, with or without meaning, can be formed such that consonants and vowels occupy alternate positions?

  1. 288

  2. 576

  3. 1,152

  4. 2,304
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

QUESTION has 8 letters: Q, U, E, S, T, I, O, N. Consonants: Q, S, T, N (4). Vowels: U, E, I, O (4). To alternate, we can have CVCVCVCV or VCVCVCVC. For CVCVCVCV, 4! ways for consonants and 4! for vowels = 24 * 24 = 576. For VCVCVCVC, 4! * 4! = 576. Total = 576 + 576 = 1152.

AI explanation

The word QUESTION has 4 vowels and 4 consonants. If vowels occupy the odd positions, they can be arranged in 4 factorial ways, and the consonants in the even positions can be arranged in 4 factorial ways. The same applies if consonants occupy the odd positions and vowels occupy the even positions. Therefore, the total number of words is 2 times 4 factorial times 4 factorial, which equals 2 times 24 times 24, giving 1152.

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