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Given $n$ players and $m$ baskets. Each player has random distinct label from the set $\{1, ..., n\}$. Each player $i$ selects a set of baskets $B(i)$ uniformly randomly with probability $p$. Then, each player $i$ puts a paper with his/her label in all the baskets in $B(i)$. A player $i$ win a basket $j \in B(i)$ if the paper he puts in $j$ is the smallest.

What is the expected number of winners ?

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Find the probability player $i$ wins a particular basket.

Use this to find the probability player $i$ wins at least one basket.

Add these probabilities.

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