X is the number of fives observed and Y is the number of sixes observed.

I created a table

P[SUB]X,Y[/SUB](x,y) | y=0 | y=1 | y=2 | y=3 | y=4 | P[SUB]X[/SUB](x) |

x=0 | ||||||

x=1 | 0 | |||||

x=2 | 0 | 0 | ||||

x=3 | 0 | 0 | 0 | |||

x=4 | 0 | 0 | 0 | 0 | ||

P[SUB]Y[/SUB](y) |

I understand the method of calculating the PMF, I'm having counting issues, calculating the probability for each part. I believe the zeros are placed correctly? If 4 fives are observed you can't have more than 0 sixes observed and vice versa.

For example, how do I calculate the probability of 2 fives observed and 2 sixes observed? Please help, thanks.