Question

How many three-digit numbers are there with no digit repeated ?

Answer 1

We have to form all possible 3-digit numbers with
distinct digits.
We cannot have 0 at the hundred's place. so, the hundred's place can be filled with
any of the 9 digits 1,2,3,4...., 9. so, there are 9 ways of filling the hundred's place. Now, 9 digits are left including 0, so, ten's place can be filled with any of the remaining 9 digits in 9 ways. Now, the unit's place be filled with in any of the remaining 8 So, there are 8 ways of filling the unit's place. Hence, the total number of required numbers= $9\times 9\times 8=648$