Question

How many $4-$digit numbers can be formed by using the digit $1$ to $9$ if repetition of digits is not allowed?

Answer 1

Finding $4-$digit number using digits $1$ to $9$ when repetition is not allowed.
Total number $\left(n\right)=9$
Required digits $\left(r\right)=4$
$\therefore$ required $4-$digit number $={}^9{P}_4$
$=\frac{9!}{(9-4)!}=\frac{9!}{5!}=\frac{9\times 8\times 7\times 6\times 5!}{5!}=9\times 8\times 7\times 6=3024$