hard combinatorics problem

[Guest]

There are 200 balls/cards whatever you call them
We mark 20 of these, let's say there are 20 red cards in a bag and the rest of the cards are black (180 black cards)
These 200 cards are going to be distributed randomly to 10 different bags, each bag will contain 20 random cards
how can I calculate the possibility of 2 red cards getting into the same bag?
My friends said I have to calculate the possibilities this not happening and subtract them from 1 but I'm not sure how