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Africa 101 · Apr 8, 2007, 05:23 PM

When rolling a red die and a green die, how many combinations of rolls will add to 6?

galactus · Apr 8, 2007, 05:31 PM

You can use the following generating function to find the number of ways two die will sum to 6.

$\left(\sum_{k=1}^{6}x^{k}\right)^{2}$

Expand and look at the coefficient of x^6. That's your answer.

Actually, it'd probably be easier for you to just write them out. There aren't that many.

G-1, B-5
G-2, B-4
B-1, G-5
G-4, B-2
B-3, G-3

That's about it.

The aforementioned generating function works nice if the sum needed is large, such as how many ways can 5 dice sum to 24? Now, that's a 'whole nuther' matter. However, if you used it you would see the 5x^6.