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Assume that she has 3 possible destinations: Oregon, Utah, and Colorado. There a

ID: 3143967 • Letter: A

Question

Assume that she has 3 possible destinations: Oregon, Utah, and Colorado. There are 4 ski areas in Oregon with 4 available times for 3 of the areas, and 2 times for the other area. There are 5 ski areas in Utah with 3 available times for 4 of the areas, and 4 times for the other area. There are 4 ski areas in Colorado with 1 available times for 3 of the areas, and 2 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time.

How many possible plans are there?

Incorrect answer: 45,49

Explanation / Answer

The destinations are Oregon, Utah, Colorado.

Oregon: Total areas are 4

4 available times for 3 areas means total vacancies in 3 areas are 12

2 available times for other 1 area means total vacancies in 1 area is 2

Therefore total vacancies in Oregon are 12 + 2 = 14

Utah: Total areas are 5

3 available times for 4 areas means total vacancies in 4 areas are 12

4 available times for other 1 area means total vacancies in 1 area is 4

Therefore total vacancies in Oregon are 12 + 4 = 20

Colorado: Total areas are 4

1 available time for 3 areas means total vacancies in 3 areas are 3

2 available times for other 1 area means total vacancies in 1 area is 2

Therefore total vacancies in Oregon are 3 + 2 = 5

Total vacancies in all Oregon, Utah and Colorado are (14 + 20 + 5) = 39