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?
There are 10 possibilities for the first digit. After the first digit has been chosen, there are 9 possibilities for the second digit.  After these two digits have been chosen, there are 8 possibilities for the third digit and after the first three digits have been chosen there are 7 possibilities for the last digit. The total number of possible settings is $10\cdot 9\cdot 8\cdot7=\boxed{5040}$.