In a game of Yathzee, five balanced dice are rolled simultaneously. Find the probabilities of getting:
a) two pairs
b) three of a kind
C) a full house (three of a kind and a pair)
D) four of a kind
Please help me with this question. I don't understand this game.
Best Answer
I will do A for you, and then I hope you can figure the rest yourself. We first need to choose the number of dots for the pairs. This can be done in ${6 \choose 2} =15$ ways. Then we want to choose a number of dots for the single, this can be done in 4 ways. The number of reorderings of these is $\frac{5!}{2!^2}=30$. This gives in total $15\cdot4\cdot30=1800$ ways to get two pairs. The total number of dice throws is $6^5=7776$. So the odds of getting two pairs is $\frac{1800}{7776}=0,231$.