What is the probability of x people being part of a group of y people picked out of z people

Actually, all I really need is the formula. If, for example, 10,000 people are picked out of a group of 1,000,000 people, what is the formula for the probability that 5 specific people will be part of that group of 10,000?

Specifying that x be among the y picked out of z.
There are C(z,y) total ways to pick them.

There is 1 way to pick the x people--they are specified.
There are C(z,y-x) to pick the remainder of the y people.

So the probability you are looking for is C(z,y-x) / C(z,y)