i. The worcester line makes 10 inbound trips, 4 of which are express and 6 are local. In how many ways can we order the trips as a sequence of either express or local trips. For example, LLEELLEELL is one possibility. ii. A train engine is to be connected with either 3, 4, or 5 passenger cars chosen from 7 available passenger cars. Assuming the passenger cars are all numbered, and that the same cars linked together in a different sequence constitutes a different train, how many possible trains could we form? iii. Suppose an inbound train starts at station 1 and ends at station 10. The local train makes all 8 intermediate stops at stations 2 through 9. An express train is any inbound train that makes no more than 3 intermediate stops. (The starting and ending station do not count.) How many different valid express train trips are possible