Class 11

Math

Algebra

Permutations and Combinations

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

$□□□HTO$

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

$⇒$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.

$⇒$Similarly, to fill $Hundreds$ of places, we have $7$ digits remaining.

So, hundreds can be filled by $7$ ways.

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