Solved

# Wildcards and Statistics

Posted on 2006-05-17

I have a stack of numbered and colored cards.

Colors are red, blue, green. Numbers are 1, 2, 3.

There are four copies of each number in each color (a total of 36 numbered cards).

A winning hand contains:

- Four 1's and four 3's, all of the same color (that's 8 red cards OR 8 blue cards OR 8 green cards)

- Three pairs of 2's, one in each color (that's 2 red cards AND 2 blue cards AND 2 green cards)

There are 8 jokers/wildcards, which may be used in place of any of the numbered cards.

If I draw 14 cards at random, how do I find the probability of drawing a winning hand?

If there were no jokers, then the number of ways to draw a winning hand is (8c8 * 3c1) * ((4c2)^3 * 3c3) = 648, and the number of ways to draw any hand is 36c14 = 3 796 297 200, yielding a probability of 1.78E-71.

But I don't know how to add in the jokers.