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 probability for each of the following:

(a) All hip surgeries are completed before another type of surgery.

(b) The schedule begins with a hip surgery.

(c) The first and last surgeries are hip surgeries.

(d) The first two surgeries are hip surgeries.