I just discovered these boards about a month ago but this is my first post! I've been toying with the design of a board game for about two months now but I'm having a problem finding some probabilities relating to cards. At first I thought this would be fairly simple to figure out by reading a few websites that covered collection probability, but it has me stumped. Here is my example:

40 card deck

6 cards with a diamond on them

5 card hand

What is the probability of having 2 diamonds in the 5 card hand? This is assuming no other players have drawn any cards from the deck.

Can someone explain in relatively simple terms how to find this? I've spent hours looking at websites that deal with probability to no avail. They always seem to use an example where you have to have certain cards in every slot of your hand, vice this example where 3 slots can be any card. Any help would be appreciated!

-Sgraffite

Thank you guys for the quick responses!

Either was fine really as it was just for me to learn from. With the steps that Sebastian posted I'm pretty sure I can find any probability for my game that I would need to. This will be a great help in balancing, thanks again guys :)

-Sgraffite