Multiple choice

In how many other ways can the letters of the word $'MULTIPLE'$ be arranged Without changing the order of the vowels

  1. $3359$
  2. $4400$
  3. $3524$
  4. $5200$
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A Correct answer
Explanation

Word MULTIPLE has 8 letters: M, U, L, T, I, P, L, E. Vowels are U, I, E (3). Consonants are M, L, T, P, L (5). Total arrangements = 8! / 2! = 20160. If vowels must stay in order, we divide by 3! = 6. 20160 / 6 = 3360. Subtracting the original arrangement gives 3359.

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