How many 3 digits with 3 Distinct digits are there from 100-1000?

The question is: How many 3 digit numbers are there with 3 distinct digits from 100 through 999? (1000 is too big)

The answer is 648.

If you break 100 to 999 into groups of 100 numbers, 100 to 199, 200 to 299, etc. and eliminate the numbers that have 2 or more of the same digit, you'd eliminate 100, 101, 110,111,112,113,114, 115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191, and 199. That means you have eliminated 28 of those 100 numbers. 72 numbers times each of the 9 groups of a hundred numbers gives 648 numbers.

You can get the same thing by using the Fundamental Counting Principle. For the hundreds column, you only have a choice of 9 numbers, the digits 1 through 9. The next column can have any of the remaining 9 digits from 0 through 9 that were not already chosen. Since 2 of the 10 digits were already used, the third spot can have any of the remaining 8 unused digits.

9 x 9 x 8 = 648

I come up with 863