Multiple choice

In how many ways can the letters of the word "SCHOOL" be arranged such that no two vowels appear together?

  1. 240

  2. 210

  3. 340

  4. 360
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

SCHOOL has 6 letters: S, C, H, O, O, L. Consonants: S, C, H, L (4). Vowels: O, O (2). Arrange consonants: 4! = 24. Spaces for vowels: _ S _ C _ H _ L _. 5 spaces for 2 vowels. Arrangements = 24 * 5P2 / 2! = 24 * 10 = 240.

AI explanation

The word SCHOOL has 6 letters with O repeated twice, meaning the 4 consonants can be arranged in 4! / 2! = 12 distinct ways. Arranging the 4 consonants creates 5 available gaps (including the ends) to place the 2 vowels so they do not touch; the vowels can be placed in these gaps in 5P2 = 20 ways. Multiplying the consonant arrangements by the vowel placements gives 12 multiplied by 20, which equals 240 ways.

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