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.
Thanks,
Rico (Ps English isn't my first language)
Best Answer
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.