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There are 10 kids at an orphanage and there are n possible homes. Each childs home is randomly chosen from the n possibilities. 1. If

There are 10 kids at an orphanage and there are n possible homes. Each childs home is randomly chosen from the n possibilities.

1. If n = 10 what is the probability each child gets assigned to a different home?

2. Using Stirlings Formula and the Taylor expansion, find the approximation for the smallest n such that each child gets a different home with probability larger than .99

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