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How Many Words Can Be Formed by Arranging the Letters of the Word 'Mumbai' So that All M'S Come Together?

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Question

How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?

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Solution

The word MUMBAI consists of 6 letters taht include two Ms.
When we consider both the Ms as a single entity, we are left with 5 entities that can be arranged in 5! ways.
Total number of words that can be formed with all the Ms together = 5! = 120

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Factorial N (N!) Permutations and Combinations
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Chapter 16: Permutations - Exercise 16.5 [Page 43]

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R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.5 | Q 6 | Page 43

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