Multiple choice

The number of permutations that can be made from the letters of the word "HOTEL" so that the vowels may occupy the even places is

  1. $2$
  2. $6$
  3. $12$
  4. $36$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

HOTEL has 5 letters: 2 vowels (O, E) and 3 consonants (H, T, L). Even positions are 2 and 4. There are 2! ways to arrange vowels in even spots and 3! ways to arrange consonants in the remaining 3 spots. Total = 2 * 6 = 12.

AI explanation

The word HOTEL has 5 letters with 2 vowels (O, E) and 3 consonants. The even places are the second and fourth positions, so the 2 vowels can be arranged in these places in 2P2 = 2 factorial = 2 ways. The 3 consonants can be arranged in the remaining 3 places in 3P3 = 3 factorial = 6 ways. The total number of permutations is the product of these two values, which is 2 times 6 = 12.

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