(a) A businessman in Chicago is preparing an itinerary for a visit to five major

Question

(a) A businessman in Chicago is preparing an itinerary for a visit to five major cities. Each city will be visited once and only once. The distance travelled, and hence the cost of the trip, will depend on the order in which he plans his route. How many different itineraries (and trip costs) are possible?

(b) An interior decorator must furnish two offices. Each office must have a desk, a chair, a file cabinet and 2 bookcases. At a local office furniture store there are 6 models of desks, 8 models of chairs, 4 models of file cabinets and 10 models of bookcases, all of which are compatible. (Any desk can be matched with any chair, etc.) How many choices does the decorator have if he wants to select two desks, two chairs, two file cabinets and four bookcases if he doesn't want to select more than one of any model?

(c) Heidi prepares for a test by studying a list of 15 problems. She can solve nine of them. For the test, the instructor selects seven questions at random from the list of fifteen. What is the probability that Heidi can solve all seven problems on the test?

(d) Steve takes either a bus or the subway to go to work with probabilities 0.25 and 0.75, respectively. When he takes the bus, he is late 40% of the days. When he takes the subway, he is late 30% of the days. If Steve is late for work on a particular day, what is the probability that he took the bus?

Explanation / Answer

A) here we have to simply find how many different ways the business man can visit the five major cities

Which can be calculated by 5! =5*4*3*2*1=120

Hence there are 120 different itineraries (and trip costs) that are possible

I can provide you with answer of one question at a time, please repost the other questions separately

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