No Repeated Digits
How many three digit numbers have three distinct digits?
Details and assumptions
The number is a two digit number.
Digits are distinct if they are not equal.
The answer is 648.
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1 solution
If a three-digit number has no repeated digit, we have 9 choices for the first digit (since the first digit cannot be 0), 9 choices for the second digit (since it can't be the same as the first digit), and 8 choices for the third digit (since it can't be the same as either other digit). By the rule of product, there are 9 × 9 × 8 = 6 4 8 three-digit numbers with no repeated digits.