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  4. Total number of words that can be formed using all letters of the word 'BRIJESH' that neither begins with I nor ends with B is equal to

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Q. Total number of words that can be formed using all letters of the word 'BRIJESH' that neither begins with I nor ends with $B$ is equal to

Permutations and Combinations

Solution:

Total words, without any restriction $=7 !$
Total words beginning with $I=6 !$
Total words ending with $B=6 !$
Total words beginning with I and ending with $B =5 !$
Thus, total number of required words $=7 !-6 !-6 !+5 !$
$=7 !-2(6 !)+5 !$