How many numbers are there between 100 and 999 in which all three digit numbers are different?

Answer 1

There are 9 possible numbers for the first digit (one of {1, 2, ..., 9});

with 9 possible digits for the second digit (one of {0, 1, 2, ..., 9} which is not the first digit));

with 8 possible digits for the third digit (one of {0, 1, 2, ..., 9} less the 2 digits already chosen);

This there are 9 × 9 × 8 = 648 such numbers.

Answer 2

There are 648 such numbers.