Hi,

I would like to calculate the probability of getting the same outcome twice when throwing two dice in the following way. First die i throw 4 times and second die 3 times. So the total sample space is

$\displaystyle S = 6^4 \times 6^3$

the question is how many casaes there are that have exactly 2 matching pairs of outcomes in S.

know this i probably a simple problem but I just cannot wrap my head arround it.

thank you