How many permutations of the letters of the word 'MADHUBANI' do n… - Vidyadip

Question

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

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Answer

MADHUBANI Total number of words that ends with letter $\text{I}=\frac{8!}{2!}$ $=8\times7\times6\times5\times4\times3$ $=50\times30\times12$ $=20160$If the words starts with Mand end with I, there are 7 space left for 7 letters.
Number of words that starts with M and end with $\text{I}=\frac{7!}{2!}$
$=7\times5\times4\times3$ $=42\times60$ $=2520$Number of words which do not start with M but end with I
$= 20160 - 2520$ $= 17640$ Required number of words = 17640

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