2.6.12 Similar to the hospital schedule in Example 2.9, 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. c. The first and last surgeries are hip surgeries given that knee surgeries are scheduled in time periods 2 through 4. d. The first two surgeries are hip surgeries given that all knee surgeries are last.