How many ways can you get a sum of 7 or more from a roll of two dice?

Question

anonymous · Answer

Since there are only $6\times 6=36$ combinations total, it wouldn't be hard to count which add up to 7.

anonymous · Answer

Yeah, 16 ways, starting with (4,3), (4,4), (4,5).....(5,6), (6,6).

anonymous · Answer

But i need to know how to display it algebraically

anonymous · Answer

18 ways, my apologies

anonymous · Answer

Okay, well consider what the first die is, and how many ways you can get a sum > 6 in each case.  With 6 there are six ways, 5 there are 5, 4, there are 4, etc.  So it's just:
$$\large \sum_{k=1}^nk^2 = \frac{1}{6}n(n+1)(2n+1)$$In our case, $n=6$.

anonymous · Answer

Wow, so that is the binomial type function that represents t. Thanks you very much.

anonymous · Answer

Is there some other combinatoric rule you are supposed to use?

anonymous · Answer

I don't believe so. We are just working with permutations, combinations and factorials