In a game of Yathzee, five balanced dice are rolled simultaneously. Find the probabilities of getting: 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.
 A: 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 $\frac{1800}{7776}=0,231$. 
A: The dice are normal six-sided dice. The rest seems rather self-explanatory; for detailed rules of the game see its Wikipedia page.
But for some  detail: 


*

*two pairs would mean you roll, say, $2,2,5,5,6$ so a pair of $2$s and a pair of $5$s.

*three of a kind means you roll the same number three times so $4,4,4,5,6$ for instance. 

*full house means a pair of one number and three of a kind of another number, so $(1,1,1, 5, 5)$ for example. 

*four of a kind means you roll the same number four times so $4,4,4,4,6$ for instance. 
Note that there is no requirement the numbers appear in this order in the rolls I just grouped them for easy reading.
