Assume that she has 3 possible destinations: Oregon, Utah, and Colorado. There a
ID: 3143966 • 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?
Explanation / Answer
Let us first consider Oregon.
There are 4 available times for 3 of the areas and 2 for the remaining.
=> Total number of plans in Oregon = 4*3 + 2 = 14
Now let us consider Utah
There are 3 available times for 4 of the years and 4 for the remaining.
=> Total number of plans in Utah = 3*4 + 4 = 16
Similarly for Colorado
There is 1 available time for 3 of the areas and 2 for the other area
=> Total number of plans in Colorado = 1*3 + 2 = 5
Therefore the grand total number of possible plans = 14 + 30 + 5 = 49