Collecting a Complete SetDate: 03/15/2000 at 07:18:55 From: Keith Butler Subject: Probability/Combinations I have a very large box filled with 8 different frying pan handles in equal proportions. What is the probability that I will have to remove 32 handles before I get a complete set? I'm thinking combinations but the formulas I find don't seem to apply, and when I work it through it my head, even with a smaller number of handles, my brain blows up by the potential number of combinations. Thank you very much, Keith Date: 03/15/2000 at 12:07:54 From: Doctor Anthony Subject: Re: Probability/Combinations The number of possible results is 8^32 (i.e. there are 8 possible results each time a handle is chosen.) A simple model will be that of throwing an 8-sided die 32 times (n = 32) and finding the probabilities of N = 1, 2, 3, 4, 5, 6, 7, 8 different numbers. This can further be modeled by thinking of distributing 32 balls into N = 1, 2, 3, 4, 5, 6, 7, 8 urns. To deal with equi-probable outcomes we must use the T(n,m) function. For an explanation of the T(n,m) function, see: Collecting a Set of Coupons http://mathforum.org/dr.math/problems/amal2.2.3.00.html - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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