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That dependsThat depends upon whether you are allowed to repeat numbers. If you are allowed to repeat, that means that all seven digits (say 1 through 7) can be used in each of the four positions of your combination, even if a digit has been used in another position. That means there are 7 x 7 x 7 x 7 = 74 = 2401 possible combinations for your lock.

But if you are not allowed to repeat, that means that every time you pick a digit for one spot, there will be one less digit for the next, and one less for the next, and so on. So, the first number can have seven possibilities, the second can have six, the third can have five, and the last can have four possible digits. That means there are 7 x 6 x 5 x 4 = 840 possible combinations for your lock, only about a third as many.

Check out the related link at MathsIsFun. It has very good information on this subject.

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That is true for PERMUTATIONS, but not for combinations. In a combination, the order of digits does not matter so that 1234 is the same as 1342 or 4213 ext.

As a result you have 7C4 = 7!/[4!*(7-4)!] = 7*6*5/(3*2*1) = 35 combinations - not 2401.

Incidentally, nCr is the notation for the number of combinations of r objects taken from n objects - exactly what the question asked for.

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