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To find the number of ways to roll a total of 18 with 5 dice, we can use the generating functions or combinatorial counting techniques. Each die can roll a number from 1 to 6, and we need to solve the equation ( x_1 + x_2 + x_3 + x_4 + x_5 = 18 ) where ( 1 \leq x_i \leq 6 ). By transforming the variables (e.g., letting ( y_i = x_i - 1 )), the problem can be approached using stars and bars or dynamic programming methods. The total number of combinations that yield 18 is 170.
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How many ways can you roll number 6 with 2 dice?
The probability is 1 in 36
How many ways can you roll a 7 with 2 dice?
6
How many ways can you roll a six with 2 dice?
12
How is it possible to not roll a 6 with 6 dice?
if you are talking about getting a roll that totals 6 - there is only one way to roll that - get all ones. as such there are 6^6 -1 = 46656 -1 = 46655 other ways to roll the dice. so the odds of not rolling a total of 6 with 6 dice is 46655/46656 = .~99.997857%. If you are talking about not rolling a 6 on ANY of the dice, there are 5 ways to roll each die that will give you something other than 6 so the number of ways to not roll any 6's is 5^6 = 15625. That means the odds of not rolling any 6's on 6 dice is 15625/46656 = ~38.489798%
When rolling two dice what is the probability of the sum being a factor of twelve?
That's a very nice problem !Total number of possible outcomes with two dice = 36.Factors of twelve = 1, 2, 3, 4, 6, and 12.Number of ways to roll a '1' = zeroNumber of ways to roll a 2 = 1 . .. . (snake-eyes)Number of ways to roll 3 = 2 . . . . . (1,2 and 2,1)Number of ways to roll 4 = 3 . . . . . (1,3 / 2,2 and 3/1)Number of ways to roll 6 = 5 . . . . . (1,5 / 2,4 / 3,3 / 4,2 and 5,1)Number of ways to roll 12 = 1 . . . . (box-cars)Total number of successful rolls = 12Probability = 12/36 = 1/3 = 33 and 1/3 percent.
