[quote name=\'TLEberle\' date=\'Feb 21 2005, 09:04 PM\']I'm trying to figure out what the odds are of winning the bonus round of "Shop 'til You Drop." (Some people collect bottle caps, I mess around with my graphing calculator. Go figure.) I'm working based on the following assumptions: the team gets all six boxes, and one box will guarantee a victory, no matter what is inside the other five.
Using my trusted TI-86, I know that there are 3,003 different ways to pick six boxes out of a possible 14. Unfortunately, that's about all I've got. I think the next step is to figure out how many different ways you can combine that one box with five others, but I don't know how.
If you can help me out, I sure would appreciate it. Even a nudge in the right direction would be good.
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As with other probability questions we've seen here, you're overcomplicating this. If you pick six boxes of 14, and one of them gives a win, the odds are 6 out of 14, yes?
While it's true that you can lose when getting the big box, and you can win without getting it, these events occur no more than once or twice a season, and tend to cancel each other out. So they're statistically insignificant.