Number of Combinations

A combination lock has 3 dials. Each of the dials has numbers ranging from 0-4. How many different combinations are possible with the lock?

The number of different combinations is equal to the maximum number that can be formed with numbers 0 to 4 having 3 digits. This means that we are numbering the possible combinations in base 5 This number is

$444 (base 5) = 4*5^2+4*5+4 = 124 (base 10)$ different combinations.