A three digit number, if the digits are unique

math_celebrity · Oct 14, 2020

For our first digit, we can start with anything but 0. So we have 9 options
For our second digit, we can use anything but 9 since we want to be unique. So we have 9 options
For our last digit, we can use anything but the first and second digit. So we have 10 - 2 = 8 options

Our total 3 digit numbers with all digits unique is found by the fundamental rule of counting:
9 * 9 * 8 = 648 possible 3 digit numbers