I've been going in circles trying to work out the solution to this problem:

Suppose that 10 cards, of which 7 are red and 3 are green, are put at random into 10 envelopes, of which 7 are red and 3 are green, so that each envelope contains one card. Determine the probability that exactly k envelopes will contains a card with a matching colour (k= 1,2,......,10)

By intuition I realise k cannot be less than 4 but then I get confused.

Any help would be appreciated!