Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If you are given 3 standard 6-sided dice, and are asked to pick the order of the numbers that will appear; what is the probability that you will win, given that order DOES matter?

share|cite|improve this question
What do you mean by "pick the order of the numbers"? – joriki Oct 14 '12 at 17:38
You choose what numbers are going to be rolled, and the order they are going to show up in. – jasouth Oct 14 '12 at 17:58

I guess, it's still 1/216. Similar to choosing a number between 000 and 999 with odds 1/1000.

share|cite|improve this answer

How many different orderings are there? clearly $3!$:


where a,b,c are the first, second and third throw.

Is some order more likely than others? No, because of symmetry.

So the answer would be $\frac{1}{6}$.

The only thing that you did not clarify is what you want to do with ties... (I ignore them in this case)

share|cite|improve this answer
There are $3!=6$ different orders of three different numbers, corresponding to their $3!$ different permutations. – joriki Oct 14 '12 at 17:41
@joriki I corrected it before you commented, but I think the OP might want to clarify what he meant by picking the order... I gave my own interpretation - that he is trying to guess the rank. – Bitwise Oct 14 '12 at 17:44

The size of the probability space is $6^{3}$. The event that you guess the right sequence of numbers has size 1. Thus, the probability is $\frac{1}{216}$, in fact only 1 of the possible sequence is the right one (given that order matters).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.