Problem 2. The city of Townsville wants to start a bus system with 27 bus routes. Each route
needs exactly 1 bus to operate it. There are 3 types of buses that could be purchased: standard
city buses, electric buses, and long-distance coach buses.
(a) How many ways are there to assign one type of bus to each route?
(b) How many ways are there to purchase 27 buses out of 3 types of buses? (e.g. one way is 14
city buses, 13 electric buses, and 0 coach buses).
(c) Suppose that you purchase 10 city buses, 12 electric buses, and 5 coach buses. How many ways
are there of assigning these buses to the 27 routes?