The National Resident Matching Program (NRMP) is a service provided to match graduating medical students with residency appointments at hospitals. After students and hospital officials have evaluated each other, they submit rank-order lists of their preferences to the NRMP. Using a matching algorithm, the NRMP then generates final, nonnegotiable assignments of students to the residency programs of hospitals (www.nrmp.org). Assume that three graduating medical students (#1, #2, and #3) have applied for positions at three different hospitals (A, B, and C), each of which has one and only one resident opening.
a. How many different assignments of medical students to hospitals are possible? List them.
b. Suppose student #1 prefers hospital B. If the NRMP algorithm is entirely random, what is the probability that the student is assigned to hospital B?