Getting a straight in YAMB
June 26th, 2015 at 6:45:37 AM
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Hello,
Could someone help me regarding this task. I have a problem I'm trying to solve.
What is probability to get a straight (first hand) which can be (12345 or 23456) out of 6 dices. I read numberous threads but could find an answer regarding six dices (only five). An explanation would be helpfull.
I'm new to the forum so my apology for creating this new thread.
Could someone help me regarding this task. I have a problem I'm trying to solve.
What is probability to get a straight (first hand) which can be (12345 or 23456) out of 6 dices. I read numberous threads but could find an answer regarding six dices (only five). An explanation would be helpfull.
I'm new to the forum so my apology for creating this new thread.
June 26th, 2015 at 8:56:14 AM
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I am assuming that something like 123345 counts.
There are 66 = 46,656 different ways of rolling six dice. (To make it easier to visualize, assume the dice are six different colors.)
There are 6! = 720 ways to roll 1,2,3,4,5,6 (123456, 123465, 123546, 123564, ..., 654231, 654312, 654321).
For 1,2,3,4,5,x (where x can be any number from 1 to 5), there are 5 values for the pair, 15 for the locations of the two dice in the pair (11xxxx, 1x1xxx, 1xx1xx, ..., xxx11x, xxx1x1, xxxx11), and 24 permutations of the remaining 4 numbers, so there are 5 x 15 x 24 = 1800 ways to roll this.
There are also 1800 ways to roll 2,3,4,5,6,x.
There are a total of 720 + 1800 + 1800 = 4320 ways to roll a five-number straight with six dice.
The probability = 4320 / 46656 = 5 / 54.
There are 66 = 46,656 different ways of rolling six dice. (To make it easier to visualize, assume the dice are six different colors.)
There are 6! = 720 ways to roll 1,2,3,4,5,6 (123456, 123465, 123546, 123564, ..., 654231, 654312, 654321).
For 1,2,3,4,5,x (where x can be any number from 1 to 5), there are 5 values for the pair, 15 for the locations of the two dice in the pair (11xxxx, 1x1xxx, 1xx1xx, ..., xxx11x, xxx1x1, xxxx11), and 24 permutations of the remaining 4 numbers, so there are 5 x 15 x 24 = 1800 ways to roll this.
There are also 1800 ways to roll 2,3,4,5,6,x.
There are a total of 720 + 1800 + 1800 = 4320 ways to roll a five-number straight with six dice.
The probability = 4320 / 46656 = 5 / 54.
