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Sum

Find the number of arrangements of the letters in the word BERMUDA so that consonants and vowels are in the same relative positions.

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#### Solution

There are 7 letters in the word “BERMUDA” out of which 3 are vowels and 4 are consonants.

If relative positions of consonants and vowels are not changed.

3 vowels can be arranged among themselves in ^{3}P_{3} i.e., 3! ways.

4 consonants can be arranged among themselves in ^{4}P_{4} i.e., 4! ways.

∴ Total no. of arrangements possible if relative positions of vowels and consonants are not changed = 4! × 3! = 24 × 6 = 144

Concept: Permutations - Permutations When Repetitions Are Allowed

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