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

I am working on a maths excersice and got stuck on this question where I need to calculate the probability of poker dice.

The game poker dice is played with 5 dice. It's possible to get one of the following hands:

Poker: All dice have the same value (ie 3,3,3,3,3). Four of a kind: 4 of the 5 dice have the same value (ie 3,3,3,3,1). Three of a kind Two of a kind Street: (1,2,3,4,5 or 2,3,4,5,6) Full House: (333,22) Two pair: (1,1,2,2,3)

Now I have to find the probability of these hands.

I know there are 6^5 = 7776 different throws.

For the poker there are 6 different values possible (111111,222222,333333 etc) so the probability is 6/7776

For the four of a kind theres 6*5*5 = 150 150/7776

But at the three of a kind is where I get stuck (and the other hands), wikipedia tells me there is an probability of 1200/7776. I don't know how they got the 1200.

If there is someone who could help me I would be very thankful.


Rico (Ps English isn't my first language)

share|cite|improve this question

Three of a kind:

6 ways to choose which kind it is that appears three times.

5-choose-3 (which is 10) ways to choose the three times the chosen kind appears.

5 ways for the five other kinds that could appear on one of the other two rolls, and 4 ways for the four remaining kinds to appear on the remaining roll.

6 times 10 times 5 times 4 gives 1200.

share|cite|improve this answer
  1. 3 of a kind is [wwwxy]. There are 3 ranks, wxy.
  2. Left hand side is ranks. Right hand side is number of dice (6C3)(3C1).(5C3)(2C1)(1C1) / 6^5
    • 6 ranks choose 3, there are six dice faces.
    • 3 ranks choose 1 .
    • 5 dice choose 3, you only need 3 dice to get 3 of a kind
    • 2 dice choose 1.
    • 1 dice choose 1.
  3. Solve above and you get 1200/7776.
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.