Question:medium

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

Show Hint

If vowel positions are fixed exactly, arrange only consonants. If vowel slots are fixed but vowels can interchange among those slots, multiply by the number of arrangements of vowels.
Updated On: Jun 22, 2026
  • \(60\)
  • \(360\)
  • \(600\)
  • \(300\)
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Read the constraint.
The word MULTIPLE has $8$ letters and we keep every vowel locked in its original spot.
Step 2: Identify the vowels.
The vowels are $U, I, E$; they stay fixed, so they contribute nothing to the count.
Step 3: Identify the consonants.
The remaining positions are filled by the consonants $M, L, T, P, L$, which is $5$ letters.
Step 4: Note the repetition.
Among these, the letter $L$ appears twice, so arrangements are reduced by a factor of $2!$.
Step 5: Count the consonant arrangements.
Number of ways $=\dfrac{5!}{2!}=\dfrac{120}{2}=60$.
Step 6: Conclude.
Since the vowels are fixed, the total is just $60$, which is option (1).
\[ \boxed{60} \]
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