Question: A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to schedule

A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to schedule three knee, four hip, and five shoulder surgeries. Assume that all schedules are equally likely. Determine the following probabilities:

(a) All hip surgeries are completed first given that all knee surgeries are last.

(b) The schedule begins with a hip surgery given that all knee surgeries are last.

(d) The first two surgeries are hip surgeries given that all knee surgeries are last.

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