How many different three-digit integers have exactly three different

1) Ignoring the restriction that 0 can't be in the first position: 10P3 = 10*9*8 = 720
2) Remove the possibilities with 0 in the first position (1/10th the total of 10P3): 720/10 = 72
3) Subtract the possibilities with 0 in first position from total: 720 - 72 = 648

Explanation:
There are nine different possibilities for the first digit: anything between 1 and 9. The tricky part of this question is moving to the second digit. Again, there are nine possibilities for the second digit: any number between 0 and 9, not including the one using for the first digit. Remember, a three-digit number can have zero as a digit, just not as the first digit. Finally, the third digit has eight possibilities: anything between 0 and 9 except for the two digits used already. The number of possible integers, then, is: 9 × 9 × 8 = 648, choice (B).