Multiple choice

The chance that the vowels are separated in an arrangement of the letters of the word "HORROR" is

  1. 1/2

  2. 2/3

  3. 3/4

  4. none of these
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B Correct answer
Explanation

Word 'HORROR' has 6 letters: H(2), O(2), R(2). Total arrangements = 6! / (2!2!2!) = 720 / 8 = 90. Arrangements where vowels (O, O) are together: treat (OO) as one unit, arrangements = 5! / (2!2!) = 120 / 4 = 30. Probability vowels together = 30/90 = 1/3. Probability vowels separated = 1 - 1/3 = 2/3.

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