There аre three wоrk centers (A, B, аnd C) behind the finаncial aid cоunter at a nearby university. They can each fit intо any of three office spaces (1, 2, and 3) off the corridor behind the desk. There is no student contact in these areas, only workers. The distance 1-2 is 20 feet, 2-3 is 40 feet, and 1-3 is 60 feet. The matrix of work (trips per day) at the three centers are shown in the following table. Assume that each trip must be a round-trip (from 1 to 2 and back, for example). A B C A -- 20 30 B 35 -- 25 C 30 10 -- (a) How many possible assignments are there? List them.(b) The university has decided to set them up in the order of B, C, A. Calculate the total distance traveled with that setup.(c) The university has reconsidered and wants to change the order to C, A, B. Which option is the best choice?