Multiple choice

The letters of the word "LOGARITHM" are arranged in all possible ways. The number of arrangements in which the relative positions of the vowels and consonants are not changed is

  1. $4320$
  2. $720$
  3. $4200$
  4. $3420$
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A Correct answer
Explanation

LOGARITHM has 9 letters: 4 vowels (O, A, I, O is not there, wait: L, O, G, A, R, I, T, H, M). Vowels: O, A, I (3). Consonants: L, G, R, T, H, M (6). Arrangements keeping relative positions: 3! * 6! = 6 * 720 = 4320.

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