How Many Different Combinations Are in a 3-Digit Lock?

By Staff WriterLast Updated Mar 29, 2020 2:41:50 AM ET

If each digit in a 3-digit lock contains the numbers 0-9, then each digit has 10 options, and 1,000 different combinations are possible. However, the exact number of combinations depends on how many options each digit has.

If the number of options for each digit is "x," there would be a total of x*x*x number of combinations for the lock. This is because there are x options for the first digit, x options for the second digit and x options for the third digit. Those can be combined in x*x*x different ways since the value of x can be repeated in each. In other words, if each digit has 5 options, the total number of combinations equals 5*5*5, or 125.