# Help me out on permutation and combination

I have to get all combinations of a six digit number where each digit is unique. Its clear that this combination will not have a 0 at the start as it will not be a valid six digit number. Help me on how to attack this problem.

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Are you assuming that the first digit can't be 0 or is it explicitly stated? Because in something like a PIN, 0 is a valid leading digit. – Thomas Owens Aug 31 '10 at 12:01
just count all combinations where each digit is unique, and subtract all combinations starting with 0 and having unique digits in (1,2,...9) :-) – mau Aug 31 '10 at 12:17

First, if you're talking about a six-digit number, the order of the digits matters, so it's generally not referred to as a combination.

Consider how many possibilities there are for the first digit. As you said, it cannot be zero, or you wouldn't have a six-digit number. Once there is a first digit, how many possibilities are there for the second digit? Then for the third? And so on.

The total number of six-digit numbers is the product of the various numbers of possibilities for each digit.

(As the question feels like homework to me, this is more of a hint/outline than a complete answer. If it actually is homework, please add the homework tag. If it's not homework, or if this doesn't get you to an answer, please comment with more information.)

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This seems simple : The digits will be from the set {0,1,2,3,4,5,6,7,8,9}

Number of possibility for first digit (Most significant digit) = 9 (since we can't use 0) Number of possibility for second digit = 9 Number of possibility for third digit = 8 ... Number of possibility for sixth digit (Least significant digit) = 5

Hence total possibility = 9*9*8*7*6*5.

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this is absolutely right answer – iostream007 May 10 '13 at 6:33