[quote name=\'TLEberle\' date=\'Jul 12 2004, 09:19 PM\'] While we're on the subject, does anyone have any idea how you would begin to calculate the odds of winning the car? [/quote]
It depends on how many cards you got. For simplicity, assume you have five.
There are (30 x 29 x 28 x 27 x 26) / 120 = 142,506 combinations of five cards out of the 30.
There are (28 x 27 x 26 x 25 x 24) / 120 = 98,280 combinations of cards that do not include either "CAR" card, so there are 142,506 - 98,280 = 44,226 combinations that include one or both "CAR" cards.
The combinations that win without any "CAR" cards are:
C-C-C-A-R: (11 x 10 x 9) / 6 x 11 x 6 = 10,890
C-C-A-A-R: (11 x 10) / 2 x (11 x 10) / 2 x 6 = 18,150
C-C-A-R-R: (11 x 10) / 2 x 11 x (6 x 5) / 2 = 9075
C-A-A-A-R: 11 x (11 x 10 x 9) / 6 x 6 = 10,890
C-A-A-R-R: 11 x (11 x 10) / 2 x (6 x 5) / 2 = 9075
C-A-R-R-R: 11 x 11 x (6 x 5 x 4) / 6 = 2420
Total, including all of the "CAR" card combinations: 104,726
Chance of winning: about 73.5%
That number seems a bit high, but I don't see any glaring errors in the math. Of course, not that many people get all five cards. (If you only get two cards - and it has happened - there are (30 x 29) / 2 = 435 combinations, of which (28 x 27) / 2 = 378 have no "CAR" cards, so 57, or about 13%, do.)
-- Don
