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All the letters of the word MULTIPLE are arranged in all possible ways. Find the number of arrangements in which no vowel changes its position.
- 60
- 120
- 240
- 360
Correct answer: 60
Solution
The word MULTIPLE has 8 letters: M, U, L, T, I, P, L, E. Vowels: U, I, E (positions 2, 5, 8) — these are fixed. Consonants at positions 1, 3, 4, 6, 7: M, L, T, P, L (L appears twice). Number of ways to arrange 5 consonants with one repeat (L twice) = 5!/2! = 120/2 = 60.
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