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a business has seven locations to choose from and wishes to rank only top 3 locations. How many different ways can this be done?

7 locations rank top 3 locations. How many different ways can this be done?
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4 Answers

What does "top 3 locations" mean?
If it means they have already decided which 3 of the 7 locations are "top", then you need to find how many ways you can rank 3 items.
It is 3*2*1 = 6.
Hm, ok. Here's how best to tackle this question - let's look at OPTIONS!
We have three spots to fill, spots A, B, & C. 
For spot A, there are 7 different options for what location will fill that spot. 
Regardless of which location is selected, that means that now there are only 6 options left for which location will fill spot B. 
Finally, it doesn't matter which locations fill spots A and B, there will be 5 options left to fill spot C.
In the end, we need to multiply together the number of options for spots A, B, and C.
7 * 6 * 5 = 210


Because order is important, this is a permutation. The formula for permutation nPk  is (n!)/(n-k)! in which you order k objects out of n objects. In this example, k=3 and n=7. Thus, your formula is 7!/4!.
It can be done in 7!/((3!)*(4!)) =35 ways