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The "combination" for a lock is actually a permutation, an ordered sequence. So for example: 1,2,3 and 3,2,1 are the same combination, but a different permutation. When opening a lock, obviously the sequence is important, so we want to calculate the permutations.

To do that, you multiply the number of possible choices for the first position times the number of possible choices for the second position, etc. Assuming that you can use the same number in all three positions (so 60 to the left, 60 to the right and 60 to the left is a valid choice), there are 60 x 60 x 60 possible permutations, or "combinations" for the lock = 216,000.

If you were not allowed to use the same number twice, it would be 60 x 59 x 58 = 205,320.

If you could repeat the same number, but not in sequence (so 20, 30, 20 is OK; but 20, 20, 30 is not), then there would be 60 x 59 x 59 = 208,860.

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Q: How many three digit combinations are there in a 60 digit combination lock?
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How do you solve a permutation in math?

If there are n objects to fit r places (e.g. 9 people in 7 chairs, 4 tumblers in a lock) then the number of permutations is nCk, stated as n-choose-k. This number can be calculated by the formula n!/(n - k)!. If k is equal to n, then (n - k)! = 0! = 1, and the number of permutations is simply n!. If the direction of the permutation is irrelevant (e.g. ABCD is the same as DCBA) then divide by two to cancel out the double-counting.

Related questions

How many combinations are possible for a six-digit lock?

Assuming each "digit" actually has 10 different states, there are one million combinations possible in a six-digit combination lock. However, many combination lock designs actually have fewer than 10 different states per "digit", resulting in far fewer actual combinations on such locks.


A combination lock on a suitcase has 5 wheels each labeled with digits 1 to 8 How many 5 digit combination lock codes are possible if no digit can be repeated?

6,720 combinations.


What are the possible combinations for a lock with 3 wheels and the digits 0 to 9?

The short answer is 1000. This is very easy to visualise: Simply consider each number in the combination to be a digit in a decimal number. We then end up with a three-digit number. Such a three-digit number ranges in value from 000 to 999, or 1000 unique combinations.


For her bicycle Lisa has a chain and a combination lock that has a 4-digit combination where each digit can range from 0 - 9 If adjacent digits must be different how many possible combinations can?

10x9x9x9


If a digital combination lock on a phone has 4 spaces with digits 0 to 9 How many 4 digit combination lock codes are possible if any digit can be repeate?

I would have to say 10,000 possible combinations. (0000, 0001, 0002 through 9998, 9999)


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

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.


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6 x 7 = 42 (it helps to know the multiplication tables), so the prime factors are 2 x 3 x 7, and the combination is 237


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All the possible digits (10 of them; 0-9) are multiplied by themselves by the number of digits that can be shown in the lock. (3) This is 103, or 1,000. This certainly shows why guessing is not a good way to break into a numerical lock, especially since three is a rather low number of digits for one!


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If the digits can repeat, then there are 256 possible combinations. If they can't repeat, then there are 24 possibilities.