Problem Solving

In a 3 digit number, if the first digit is not zero, the hundreds place can be filled in 9 ways.
The tens place can be filled in 9 ways and the units place in 8 ways.

So we will have 9*9*8 = 648, 3 digit numbers whose all 3 digits are different and the first digit is not zero.

The correct answer is a.

why did you pick the "8" as a third number? i understand the hundreds digit must be 9, but not tens and unit digit.

For hundreds place we can have the digits 1, 2, 3, 4, 5, 6, 7, 8, 9. These are 9 in number.
So we say that the hundreds place can be filled in 9 ways.
For the tens place we have the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 availabe and these are 10 in number but remember that 1 has already been selected for hundreds place and there has to be no repitition of digits. So we have to select from remaining 9.
Or the tens place can be filled in 9 ways.
Again for the units place, the digits availabe are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These are 10 in number, but again 1 has been selected for hundreds place and 1 for tens place and there has to be no repitition of digits.
So the units place can be filled in 10 - 2 = 8 ways.

So the total 3 digit numbers with all digits different and hundreds digit not being zero is 9*9*8 = 648.