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How Many Permutations of the Letters of the Word 'Madhubani' Do Not Begin with M but End with I?

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Question

How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?

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Solution

Number of words that only end with I = Number of permutations of the remaining 8 letters, taken all at a time =\[\frac{8!}{2!}\]Number of words that start with M and end with I = Permutations of the remaining 7 letters, taken all at a time =\[\frac{7!}{2!}\]

Number of words that do not begin with M but end with I = Number of words that only end with I -  Number of words that start with M and end with I

\[\frac{8!}{2!}\]-\[\frac{7!}{2!}\]= 17640
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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 13 | Page 43

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