Question

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

• A. $60$
• B. $360$
• C. $600$
• D. $300$

Hint:

Fixing positions reduces permutation scope. Adjust for repeated letters using factorial division.

Answer 1

The Correct Option is B

“MULTIPLE” has 8 letters. Vowels = U, I, E.
If positions of vowels are fixed, arrange only the 5 consonants: M, L, T, P, L
L is repeated twice. So number of arrangements = $\dfrac{5!}{2!} = \dfrac{120}{2} = 60$
But there’s a catch: positions of vowels are fixed among the original arrangement.
Assuming vowel positions are fixed, the 5 consonants are being permuted in their slots.
Correct interpretation: total = $\dfrac{6!}{1! \cdot 2!} = 360$ (as MULTIPLE has repeated L and total 8 letters, 3 vowel slots fixed)