Probability of sampling

[Guest]

Hi all,

I got a question concerning calculating probability in random samples.

Let's assume I have two sets of the size n(2) and n(1). Both sets are made up of the same items but can have different sizes, i.e.:

n(1) =7, set1 = [1,2,3,4,5,6,7]
n(2) = 9, set2 = [1,2,3,4,5,6,7,8,9].

From each set, I draw a random sample without replacement of the sizes k(1) and k(2).
How to calculate the probability to obtain the intersect of the size X in those 2 random samples. The 2 samples are indepent of each other P i. e:

k(1) = 4, randomSample1 = [1,2,7,6]
k(2) = 5, randomSample2 = [3,2,9,6,4]
intersect = [2,6], intersect size X = 2,

If you could point me in the direction how to calculate this accurately, I would be very grateful, for I am nothing but a sinner in the hands of the angry god of probability. If you show me the light so that I can start to atone for my sins by studying probability.

Cheers

The guest.