A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?
A)4
B)24
C)120
D)37

Question

Quizplus · Accepted Answer

Since the order in which the sales representative calls on the hospitals does not matter, we are looking for the number of combinations, not permutations. The formula for combinations is n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to choose. Here, n = 4 (the hospitals) and r = 4 (since he has to call all of them), so the calculation is 4! / (4!(4-4)!) = 4! / (4!0!) = 1. However, considering the context, the correct interpretation should be the number of permutations since the question might imply the sequence of visits matters (immaterial in the question context seems to imply the sequence can be any), which is 4! = 24.

A Sales Representative Calls on Four Hospitals in Westchester County