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To go with the Lego Movie, Lego sell minifigures of the characters from the movie.
They are sold in packets, where each packet contains one minifigure, and from the outside of the packet it is impossible to tell which minifigure is inside. There are $n$ minifigures to collect.
Assuming that each packet that my son buys is equally likely to contain any one of the minifigures, show that the expected number of packets that he needs to buy to collect the whole set is approximately $n \log n$.
[Hint: express the random variable that is the total number of packets as a sum of simpler random variables, and use linearity of expectation.]