Distinct-Digit Positive Numbers
How many 3-digit positive numbers are there that comprise of 3 distinct digits?
Details and assumptions
The number is a 2-digit number, not a 3-digit number.
2 digits are distinct if they are not the same. The number 121 is not comprised of 3 distinct digits, as the first and third are the same.
The answer is 648.
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1 solution
Since the hundreds digit cannot be 0, there are 9 possibilities to pick from. Then, there are 1 0 − 1 = 9 possibilities for the tens digit (it can be 0) as it cannot be the same as the hundreds digit. This leaves 1 0 − 2 = 8 possibilities for the units digit (it can be 0 as well) as it cannot be the same as the hundreds or the tens digit. Hence, by the product rule, there are 9 × 9 × 8 = 6 4 8 possible 3-digit numbers.