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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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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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.


YOU need to consider a differnt job bcause your answer is wrong. The correct answer it 210. 
Amanda A. | Experienced Teacher and Education Professional w/ Test-Prep ExperienceExperienced Teacher and Education Profes...
4.9 4.9 (8 lesson ratings) (8)
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


Torrey L. | Experienced academic and test preparation tutorExperienced academic and test preparatio...
4.5 4.5 (2 lesson ratings) (2)
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!.
Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (175 lesson ratings) (175)
It can be done in 7!/((3!)*(4!)) =35 ways