Multiple choice

The number of ways in which the letters of the word "VALEDICTORY" be arranged so that the vowels may never be separated is

  1. $7! 4!$
  2. $8! 4!$
  3. $7!  ^8P_4 $
  4. $4! 3!$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

VALEDICTORY has 11 letters: V, L, D, C, T, R, Y (7 consonants) and A, E, I, O (4 vowels). Treating the 4 vowels as one block, we have 8 items to arrange (7 consonants + 1 block) in 8! ways. The 4 vowels can be arranged within their block in 4! ways. Total = 8! * 4!.

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