What are the odds of rolling a small straight 12345 with five dice?

Answer 1

With 5 dice, if the first die must equal 1, the second must equal 2, and so on, then each die has a one in six chance of being the correct number. So the chance that all five of them will be correct is (1/6)5 = 1/7776

But, that's assuming that the order of the numbers must be 12345. The dice could also fall as 12453, and it would be considered a small straight. So how many ways can you get 1, 2, 3, 4 and 5? The 1 could be in any one of 5 places. Then the 2 could be in any one of the remaining 4, and so on. There are 5 x 4 x 3... ways of arranging 12345. This is also written as 5! (five factorial). 5!=120

So now, we have 120 different ways of getting a straight. Each straight, as shown at the top, has a one in 7776 chance. Therefore, (1/7776) x 120 possibilities = probability of a small straight.

(1/7776) x 120 = 120/7776 = 5/324

So there is a 5/324 probability, or about one out of 65, or 1.5% chance of getting the numbers 1, 2, 3, 4, and 5 on a single roll of 5 dice.