Coupon Collecting and Football Stickers

Although Euro 2016 is still months away from officially starting, another footballing tradition has just started: collecting football stickers. For children and adults alike the quest to complete the entire sticker album is something that takes time and money but the excitement and joy makes it worth it.

As the number of stickers in each album have dramatically increased from the first few albums produced around 40 years ago, the task of collecting all of the stickers has become much harder. Mathematically this problem happens to be a classic problem in combinatorial optimisation: the coupon-collector problem. This problem is when there is a finite number of different coupons any of which can be given to a person one at a time. In a statistical sense this is the problem of sampling with replacement. The question is then how many times do you need to sample to obtain a copy of every single sticker?

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