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June 11th, 2011, 04:42 AM  #1 
Newbie Joined: Jun 2011 Posts: 3 Thanks: 0  Supermarket card collection
Hi guys, Small question to check whether my calculations are right: Here in the Netherlands there is a grocery store that gives packages containing 4 cards with pictures of animals for every 10 euro spent in the store as a commercial stunt or something. There are 204 cards in total that can be collected. Me and my roommates are collecting them, and we have 68 cards so far. The weird thing is that we didn't get any doubles so far! I tried to do the math to calculate the chance of having no doubles, and came up with this: 204/204 * 203/204 * 202/204 * ... * 138/204 * 137/204 = ca. 0.00000319406233901451 This is a ridicilously low number, and I suspect that my math is too simple. Furthermore, if the cards are packed in a way that there are no doubles within a package of 4, this would increase the chance of this happening, but I don't know how to calculate the exact chance. Can you guys help me out? 
June 11th, 2011, 09:34 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Supermarket card collection
I get 0.0000058499 if each pack of four has no doubles: much higher than I expected, but still very small. (I'm not very sure of my methods, but it's not going to come out a lot higher than that.) Maybe there is a time component? One week they have these animals, the next week those animals, so if you buy every week the chance is 0%. 
June 12th, 2011, 02:16 AM  #3 
Newbie Joined: Jun 2011 Posts: 3 Thanks: 0  Re: Supermarket card collection
The time component would be a good explanation, indeed. I am so intrigued that I might call the store to ask whether this is the case Please tell me, how did you calculate the probability you found? 
June 12th, 2011, 07:30 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Supermarket card collection
I did it in blocks of four: 204/204 * 204/204 * 204/204 * 204/204 * 200/204 * 200/204 * 200/204 * 200/204 * 196/204 ...

June 12th, 2011, 11:40 AM  #5 
Newbie Joined: Jun 2011 Posts: 3 Thanks: 0  Re: Supermarket card collection
Smart move, wish I would have thought of that myself, now I feel stupid BTW: I regret to inform you that the 72th card was one we already had... so the magic is over. 

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