Stats geeks! Help us!

[theweaselking]

Okay, this is bothering me.

The odds of getting any result on a sum of 3d6 are exactly equal to 1/216 (the odds of any given combination of three dice) * the number of ways that combination can be made.

I can't, for the life of me, remember or find online the formula for determining the number of ways a combination can be made. It's trivial to show by brute force that theres's just one way to get an 18 and 3 ways to get a 17 and 6 ways to get a 16, but how, other than just counting 'em out, can you show that there's 27 ways to get a 10 or 11?

There's a formula for this and I can't remember it. At all. Two dice, sure. Three is driving me nuts.

Stupid factorials.

Comments

[scifantasy.livejournal.com]

Try this:

http://mathforum.org/library/drmath/view/56627.html

[theweaselking.livejournal.com]

Beautiful - calculation of coefficients is what I was missing.

[theweaselking.livejournal.com]

Of course, now I'm getting confused about how he gets to the generator function and why that works. I mean, I can SEE that it works, and I can see what he's doing, I just don't remember WHY you do that.

And I can't see how he gets
(1-x)^(-3) = (1 + C(3,1)x + C(4,2)x^2 + C(5,3)x^3 +..)

Man. I've forgotten so much.

[matgb]

Man. I've forgotten so much.

Tell me about it. Ten years ago, that made perfect sense to me, now it's numbers, letters and symbols in an incoherent order.

I understand the principles behind the probability, but not the maths. Ah well.

[jl-williams.livejournal.com]

The exact reason I am a Zen Physicist instead of a Physics teacher.

[neobitch.livejournal.com]

http://mathworld.wolfram.com/topics/ProbabilityandStatistics.html

Mathworld never steers me wrong. I hope it has an explanation for those equations for you. :)

[semi-sweet.livejournal.com]

math_help