Multiple choice

Consider the word 'QUESTION': How many 8-letter words, with or without meaning, can be formed so that all consonants are together?

  1. 5,760

  2. 2,880

  3. 1,440

  4. 720
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

QUESTION has 8 letters: Q, U, E, S, T, I, O, N. Consonants are Q, S, T, N (4). Vowels are U, E, I, O (4). Treating consonants as one block, we have 5 units (block + 4 vowels). These can be arranged in 5! ways. The 4 consonants within the block can be arranged in 4! ways. Total = 120 * 24 = 2880.

AI explanation

The word QUESTION has 4 vowels and 4 consonants. Treating the 4 consonants as a single block, we have this block plus the 4 vowels, giving 5 entities to arrange in 5 factorial ways. The 4 consonants within the block can be arranged in 4 factorial ways. Multiplying these gives 5 factorial times 4 factorial, which is 120 times 24, resulting in 2880.

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