# Re: probability; check me, someone!

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Posted by MathBard on October 20, 2002 at 17:28:42:

In Reply to: Re: probability; check me, someone! posted by Brad Paul on October 20, 2002 at 16:35:53:

: : : In a throw of 12 dice,what is the probability of obtaining a sum of 35 ?

: : I'll be as brief as possible, yet try to be clear;
: : (hate typing!); there is:
: : 1 way of getting 12: all 1's
: : 1 way of getting 13: 11 1's and a 2
: : 2 ways of getting 14: 11 1's and a 3, 10 1's and 2 2's
: : ....
: : 184 ways of getting 34
: : 197 ways of getting 35**
: : 212 ways of getting 36
: : ....
: : 252 ways of getting 42 (that's tops: so bet 42!!)
: : ....
: : 1 way of getting 72: all 6's

: : These "ways" total 6188.

: : So the probability of getting 35 is 197/6188.

: : I did printout all of them (12 to 72) but am too
: : lazy to type 'em all...

: I do not have the answer but I think your denominator should be

: 612=2176782336

: Think of just two die. If you work out a table of all the possibilities
: you have a square with 6 entries on each side. Which gives
: 62=36 possibilities for the die. Here we just have a 12
: dimensional cube.

: The hard part of the question is: How many ways can one add 12 integers
: that can range from 1 to 6 to get a value of 35 where order does make
: a difference (because of how the denominator has been calculated.)

In Mr. Boris' example he eliminated identical rolls, Mr. Paul Left them in.

TECHNICALLY there are 12 ways to roll a sum of 13.
any ONE of the twelve dice could roll a two. Here are three...
1 1 1 1 1 1 1 1 1 1 1 2
1 1 1 1 1 1 1 1 1 1 2 1
1 1 1 1 1 1 1 1 1 2 1 1
etc.
Here is where i begin to lose it. With THIS in mind there is ONE combo for 12, 12 combos for 13, and I THINK 122 combos for 14. I am not going to figure how many different ways to calculate a roll of 35 or a roll of 42 becasue i do nOt know the formula for that, but i bet one of you REAL Mathgeeks could. OR tell me i am completely off base. But that is the difference between Mr.B's and Mr.P's denominators.

MathBard
PS Remember I am an Englishgeek tring to fill the shoes of a Mathgeek 8-)

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