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Happy Sunday, I was wondering how to calculate how many combinations could be rolled in the game of Yahtzee in getting a large straight. A large straight is when you roll and the dice com out 1,2,3,4,5 or 2,3,4,5,6. Can any one give me some guidance???

Thomas
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1 Answers1

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Imagine that the dice have different colours. List the result of the tossing as a string of length $5$, like $(4,5,4, 1,6)$, alphabetically by colour.

There are $6^5$ equally likely strings.

Of these, $5!$ give you the large straight consisting of the numbers $1$ through $5$, and $5!$ give you the other large straight. This is because the numbers can occur in any order.Thus the required probability is $$\frac{2\cdot 5!}{6^5}.$$

André Nicolas
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  • Thanks for the quick response. I am not as well educated on math as I would like to be. I am not familiar with the expression 5!. – Thomas Sep 22 '13 at 17:02
  • Sorry, I should not have assumed. The number $5!$ (pronounced $5$ factorial) is $(5)(4)(3)(2)(1)$, that is, $120$. The factorial function comes up a lot in probability, and elsewhere in mathematics. The number of ways to arrange $n$ distinct objects in a row is $n!$. – André Nicolas Sep 22 '13 at 17:33
  • Thank you, your informing me that it was pronounced 5 factorial jogged some of my memory from math classes of long ago. – Thomas Sep 22 '13 at 17:47