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

Sum

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

#### 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 3P3 i.e., 3! ways.
4 consonants can be arranged among themselves in 4P4 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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Chapter 6: Permutations and Combinations - Exercise 6.3 [Page 81]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.3 | Q 9 | Page 81
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