Question

Total number of words that can be formed using all letters of the word $"BRIJESH"$ that neither begins with ${}^{\prime }{I}^{\prime }$ nor ends with ${}^{\prime }{B}^{\prime }$ is equal to

• A. $3720$
• B. $4920$
• C. $3600$
• D. $4800$

Answer 1

The correct option is A $3720$

BRIJESH

$\to$ total number of letter in the word = 7

so total words formed = 7!

let A be a set of all words bigining with 'I'

n(A) = 6!

let B be a set of all words ending with 'B'

n(B)= 6!

$A\bigcup B$ = all words beginning with I & ending with B

$n(A\bigcup B)=5!$

All words neither beginning with I nor ending

with B.

$=7!-(6!+6!-5!)$

$=7!-26!+5!$

$=3720$ Ans