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There are 65 = 7776 possible outcomes. However, if the number cubes are indistinguishable, then these represent 378 distinct outcomes.
There are infinitely many numbers and so infinitely many possible combinations.
6
There are 5,461,512 such combinations.
It depends on how many values each number is capable of having, and if repetition is allowed, and then if order is important. For example, are you rolling dice, picking Lotto balls, BINGO, etc. I am posting a link to a site called MathsIsFun, which has some good information about Combinations and Permutations.