Another question on probability.

chocolatefrog

"Suppose that ten cards, of which five are red and five are green, are placed randomly in ten envelopes, of which five are red and five are gree. What is the probability that exactly x envelopes will contain a card with a matching colour? (x = 0, 1, 2, ..., 10)"

So basically, there are six events in sample space that 5 green envelopes have 0, 1, 2, 3, 4, or 5 green cards.

Therefore p.d.f. is 1/6 for x = 0, 2, 4, 6, 8, 10, and zero otherwise?