Greetings:

A combination is an n-tuple that does not discern order. For instance, (2,3,5), (3,2,5), (5,2,3) are three ways of expressing the same combination of the numbers 2, 3 and 5. By contrast, if orderisimportant, (the order in which you write the digits in a zip code is, for instance, is important), the n-tuple is referred to as a permutation. With regard to your assertion connecting counting principles with combinations, I suspect you may have in mind the means by which we count all possible combinations on a given set taken, say, 3 at a time, as was the case in opening exaple. Indeed there are (10)(9)(8)/((3)(2)) ways of writing (combinations of) the ten digits 0,1,2,...,9 taken three at a time. If you can be more specific in your questioning, I can, perhaps, be of more assistance to you.

Regards,

Rich B.