Jack is making a list of his 5 favorite cities. He will choose 3 cities in the United States from a list of 5 candidates. He will choose 2 cities in Europe from a list of 3 candidates. How many different lists of cities, ranked from first to fifth, can Jack make?

A. 30
B. 360
C. 1,800
D. 3,600
E. 6,720
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The selection process in the United states is 5C3 and that in Europe is 3C2. (Since its a selection process we use combinations).

Therefore we get [(5*4)/(2*1) * 3] = 30 ---- Upon simplification. (1)

The Trap here would be to consider the above as the answer.

At the end of the statement it says that "different lists of cities, ranked from first to fifth".

Therefore the Cities can be arranged in 5! Ways which is 5*4*3*2*1 = 120 (2)

From (1) and (2) we get 30*120 = 3600.

Therefore option D is the answer.
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Take the task of creating a list and break it into stages.

Stage 1: Select 3 US cities
Since the order in which we SELECT the cities does not matter, we can use combinations.
We can select 3 cities from 5 cities in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways

Stage 2: Select 2 European cities
Since the order in which we SELECT the cities does not matter, we can use combinations.
We can select 2 cities from 3 cities in 3C2 ways (3 ways)
So, we can complete stage 2 in 3 ways

Stage 3: Arrange the 5 selected cities
We can arrange n unique objects in n! ways.
So, we can arrange the 5 selected cities in 5! ways (120 ways)
We can complete this stage in 120 ways.

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create our list) in (10)(3)(120) ways (= 3600 ways)

Answer: D

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