Given that 'ten different numbers' is all of them.. then including 0000, there will naturally be 10,000 combinations.
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" ... there will naturally be 10,000" only if you don't know the difference between permutations and combinations.
Orders do not affect combinations so that 1234 is the same as 4321, 1432, etc. The number of 4-digit combinationsis (10*9*8*7)/(4*3*2*1) = 210
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This question needs clarificatioh. There are 4 one digit number combinations, 16 two digit combinations, ... 4 raised to the n power for n digit combinations.
9999 + 1 * * * * * That is so wrong! There are 10*9*8*7/(4*3*2*1) = 210 combinations of 4 numbers from the set of ten 1-digit numbers, 0 1, 2, ... 9 When considering combinations, 1234 is the same as 2314 or 4123 etc. Actually... 4 numbers to be arranged with ten different possibilities each will give a total of 10^4 combinations, or 10,000.
If each number can be used only once then there are just four: 2345, 2346, 2456 and 3456. There are no others because the order of the digits does not matter in combinations.
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The answer depends on what mathematical operations are permitted and on whether or not all four number must be used.