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How Many Different Words Can Be Formed from the Letters of the Word 'Ganeshpuri'? in How Many of These Words:The Letter G Always Occupies the First Place?

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Question

How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letter G always occupies the first place?

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Solution

The word GANESHPURI consists of 10 distinct letters.
Number of letters = 10!

If we fix the first letter as G, the remaining 9 letters can be arranged in 9! ways to form the words.
∴ Number of words starting with the letter G = 9!

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Factorial N (N!) Permutations and Combinations
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Chapter 16: Permutations - Exercise 16.4 [Page 37]

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R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.4 | Q 6.2 | Page 37

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