Question

$\frac{3!}{0!}$ can also be written as which of the following?

• A. ${}^3{P}_0$
• B. ${}^3{P}_3$
• C. ${}^0{P}_3$
• D. Can't be determined

Answer 1

The correct option is B ${}^3{P}_3$

Given $\frac{3!}{0!}$

On manipulating the avove term we get,
$\Rightarrow \frac{3!}{0!}=\frac{3!}{(3-3)!}$

On comparing with the formula ${}^n{P}_r=\frac{n!}{(n-r)!}$ we get $n=r=3$

$\Rightarrow \frac{3!}{0!}=\frac{3!}{(3-3)!}={}^3{P}_3$