Advent calendar 2025
1 December
Some numbers contain a digit more than once (eg 313, 111, and 144). Other numbers have digits that are all different (eg 123, 307, and 149).
How many three-digit numbers are there whose digits are all different?
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There are 9 options for the first digit of the number (1 to 9). There are then 9 options for the second digit (0 to 9 excluding the digit already used),
and 8 options for the third digit (0 to 9 excluding the two digits already used). In total, this makes 9×9×8 = 648 numbers whose digits are all different.
