Question

Consider the word ${}^{\prime }BRIJES{H}^{\prime }$, then the total number of possible words

• A. without any restriction is $5040$
• B. that begins with $I$ is $720$
• C. that begins with $I$ and ends with $B$ is $120$
• D. that neither begins with $I$ nor ends with $B$ is $3720$

Answer 1

Answer: (A), (B), (C), (D)

that neither begins with $I$ nor ends with $B$ is $3720$

Since, we have $7$ letters
Total number of words without any restriction is $7!=5040$

For the total number of words beginning with ${}^{\prime }{I}^{\prime }$, fix $I$ at the beginning rest can be arranged as $6!$
Total words $=6!$

Similary, total number of words starting with $I$ and ending with ${}^{\prime }{B}^{\prime }$ is $5!$ $($fixing $I$ in the beginning and $B$ in the end$)$

Total words, that neither begins with $I$ nor ends with $B=$
Total number of words without any restriction - Total words that either begins with $I$ or ends with $B$
$=7!-(6!+6!-5!)=7!-2(6!)+5!=3720$