## Math Refresher – Determine Number of Possible Combinations

What is the equation to determine number of possible lock combinations?

Answer

In the simplest case, if A is the number of values a single element of a combination can have, and N is the number of elements in the combination, then the number of possible lock combinations is AN.For example: if you have a lock with a 4-digit numerical combination, any combination has 4 elements – the digits. Each digit can have 10 values – 0 through 9. So the total number of lock combinations is 104 or 10000.

Another example: if you have the typical rotating combination padlock, a combination consists of three numbers, each of which can be 0-39. So the total number of combination shere is 403 or 64000.

The calculation gets more complicated if the same number can't appear twice in the combination. In that case, there are A values for the first element, but only A-1 values for the second, A-2 values for the third, and so on. The formula in this case is A(A-1)(A-2)(…)(A-N+1) which can be written more concisely as A!/(A-N)!.

For example: if you have the same rotating combination padlock as above, but know that the numbers in the combination are all different, there are 40*39*38 or 59280 possible combinations.

Source: WikiAnswers

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