Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

dice problem

If I toss 4 dice, what is the probability that the product of the numbers is 36

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: dice problem

Hi,

Last edited by gAr (2011-12-23 03:08:25)

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: dice problem

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Wrap it in bacon

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: dice problem

gAr and TheDude how can you get it

thanks

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: dice problem

There are four ways to get 4 dice whose product is 36: 6-6-1-1, 6-3-2-1, 4-3-3-1, and 3-3-2-2.  For each of these you need to count the number of ways that they can occur.  For example, there are six ways of getting the first one: 6-6-1-1, 6-1-6-1, 6-1-1-6, 1-6-6-1, 1-6-1-6-, 1-1-6-6.  There are 24 ways of getting the second set, 12 ways of getting the third set, and 6 ways of getting the fourth set, for a total of 6 + 24 + 12 + 6 = 48.  There are 6^4 = 1296 total outcomes for four dice, so the probability is 48/1296 = 1/27.

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Wrap it in bacon