In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?

Step-by-step solution

The word MULTIPLE consists of three vowels that are placed at the 2 nd   ,   5 th and 8 th position. The three vowels can be arranged at their respective places in 3 ! ways. The remaining 5 consonants can be arranged at their respective places in 5 ! 2 ! = 60 ways ∴ Total number of arrangements = 3 ! × 5 ! 2 ! = 360