I have a game coming up I am putting in downtown Toronto, I need to know what the odds of winning are so I can plan for the prizes.
The game is comprised of 20 cards which have 10 categorize. 
To win you need to match two cards of the same category.
The first selection has no chance of winning.

The second selection has a 1 in 19 chance of winning.

What are the odds of each selection winning after that?
I need to know the chance to win selecting 3 cards, 4 cards, 5 cards and then 6 cards?

Your help is greatly appreciated....