Suppose there is a machine that has an unlimited supply of eight different kinds of stickers. Each sticker is as likely to appear as another. Given this answer the following combinatorics problems: (i) How many stickers do you need to buy to make sure that you get three of the same sticker? (ii) How many ways can five different people each get a sticker, where there is at least one person who gets a lion sticker? Given that is matters which person gets which sticker (iii) How many ways can you get five stickers from the machine where every sticker is a different kind? Given that it does not matter which order the stickers come out

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