COUNTING TECHNIQUES

1. A businesswoman in Philadelphia is preparing an itinerary for a visit to six major cities. The distance traveled, and hence the cost of the trip, will depend on the order in which she plans her route. How many different itineraries (and trip costs) are possible?

2. A brand of automobile comes in five different styles, with four types of engines, with two types of trans- missions, and in eight colors. How many autos would a dealer have to stock if he included one for each style-engine- transmission combination? How many would a distribution center have to carry if all colors of cars were stocked for each combination in the last question?

3. Find the constant term in the expansion of (x^2+1/x)^12