### Instruction: A suitcase lock has 4 dials with the digits $0, 1, 2,..., 9$ on each. How many different settings are possible if all four digits have to be different?### Response: To open the lock, I need to choose a digit for each of the four dials, and they all have to be different.
For the first dial, I have 10 choices, since any of the 10 digits can be used.
For the second dial, I have 9 choices, since I can't repeat the digit I used for the first one.
Similarly, for the third dial, I have 8 choices, and for the fourth dial, I have 7 choices.
To get the total number of possible settings, I need to multiply the number of choices for each dial.
This is because for each choice of the first digit, there are 9 choices for the second digit, and so on.
So the answer is $10 \times 9 \times 8 \times 7 = 5040$.