Multiple choice

How many five lettered words can be formed using the letters of the word $'CRANE'$ so that vowels are never together?

  1. $144$
  2. $72$
  3. $96$
  4. $120$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total permutations of CRANE is 5! = 120. Vowels are A, E. Treat (AE) as one unit, so we have 4 units (C, R, N, AE). These can be arranged in 4! * 2! = 24 * 2 = 48 ways. Vowels together = 48. Vowels never together = 120 - 48 = 72.

AI explanation

The word CRANE has 5 distinct letters, so the total number of five lettered words is 5!, which equals 120. The vowels are A and E, and treating them as a single unit gives 4 units to arrange, which is 4! ways. The vowels within the unit can be arranged in 2! ways, giving 24 ways for words where vowels are together. Subtracting this from the total gives 120 minus 48, which equals 72.

Keep practicing — related questions