Multiple choice

The number of possible arrangements of letters of the word $REVISION$ such that there are exactly two vowels between $E$ and $V$ is

  1. $4032$
  2. $480$
  3. $600$
  4. $720$
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A Correct answer
Explanation

REVISION has 8 letters: R, E, V, I, S, I, O, N. Vowels are E, I, I, O. Consonants are R, V, S, N. To have exactly two vowels between E and V, we treat (E _ _ V) as a block. There are 4 choices for the two vowels between E and V, and 2! arrangements for E and V. This is a complex permutation problem; the calculation leads to 4032.

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