Multiple choice

In how many can the letters of the word $'DETAIL'$ be arranged such that both the vowels and consonants are together

  1. $32$
  2. $36$
  3. $48$
  4. $72$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The word DETAIL has 6 letters: 3 vowels (E, A, I) and 3 consonants (D, T, L). Treating vowels as one block and consonants as one block, we have 2! ways to arrange the blocks. Within the blocks, there are 3! ways to arrange vowels and 3! ways to arrange consonants. Total = 2 * 6 * 6 = 72.

Keep practicing — related questions