(Steps Shown) In a hospital, the past record shows that there is 20 \% chance that a patient will cancel the appointment. Suppose there are 50 doctors,


Question: In a hospital, the past record shows that there is \(20 \%\) chance that a patient will cancel the appointment. Suppose there are 50 doctors, but 60 appointments has been made on a certain day, find the probability of overbooking, namely the chance that at least there is one patient who comes to the hospital but can not be seen by any doctor (all 50 doctors are seeing other patients). If the overbooking rate has to be less than \(5 \%\), how many appointments this hospital can make at most?

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