Question

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

Hint: Make 3 blank spaces of ‘Ones’, ‘Tens’, ‘Hundreds’ and start checking how many numbers can be placed without repeating.

A three digit number is to be formed from given 9 digits 1,2,3,4,5,6,7,8,9
$\begin{array}{*{20}{c}} \_&\_&\_ \end{array} \\ {\text{H T O}} \\$

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’ place, we have 7 digits remaining.
So ,’Hundreds’ places can be filled in 7 ways.
So, the required number of ways in which 3-digit numbers can be formed from the given digits is 9×8×7= 504

Note: The above problem can also be asked with repetition. In that case the answer would be 9×9×9= 729 as all the places can be filled with the same or different number i.e. all 9 digits.