A suitcase lock has 3 dials with the digits $0, 1, 2,..., 9$ on each. How many different settings are possible if all three digits have to be different?
For the first dial, I have 10 choices, since any digit from 0 to 9 is possible. For the second dial, I have 9 choices, since I can't repeat the digit I already chose for the first dial. For the third dial, I have 8 choices, since I can't repeat the digits I already chose for the first and second dials. So the total number of settings is the product of these choices: $10 \times 9 \times 8 = 720$. 