Multiple choice general knowledge math & puzzles

The letters of the word ‘EQUATION’ are arranged in a row. Find the probability that all vowels are together

  1. 1/14

  2. 1/21

  3. 1/8

  4. 2/21

  5. none
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A Correct answer
Explanation

EQUATION has 8 letters (3 vowels: E,U,A,OI and 5 consonants: Q,T,N). Treating all 4 vowels as one block gives 5! arrangements of blocks, and 4! arrangements within the vowel block. Total with vowels together = 5! × 4! = 120 × 24 = 2880. Total arrangements of 8 letters = 8! = 40320. Probability = 2880/40320 = 1/14.

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