Question

How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

Answer 1

A three digit number is to be formed from given $9$ digits $1,2,3,4,5,6,7,8,9$.
$\square \square \square HTO$

$\Rightarrow$Now, there are $9$ ways to fill $Ones$ place.

$\Rightarrow$Since repetition is not allowed, so $Tens$ place can be filled by the remaining $8$ digits.
So, tens place can be filled in $8$ ways.

$\Rightarrow$Similarly, to fill $Hundreds$ of places, we have $7$ digits remaining.
So, hundreds can be filled by $7$ ways.

$\Rightarrow$So, the required number of ways in which three-digit numbers can be formed from the given digits is $9\times 8\times 7=504$