Question

The number of words can be formed using all letters of the word EQUATION, using each letter exactly once is

• A. $40220$
• B. $40320$
• C. $40440$
• D. None of these

Answer 1

The correct option is B $40320$

Number of letters in word 'EQUATION'=8

$n=8,$

If all letters of the word used at a time

$r=8,$

Different numbers formed ${}^n{p}_r$

${=}^8{p}_8$

$\frac{8!}{(8-8)!}$

$=\frac{8!}{0!}$

$=8!$

$=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1$

$=40,320.$

$\therefore$ Different number formed $=40,320.$