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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?

### 4 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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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.
7*6*5=210
Amanda A. | Experienced Teacher and Education Professional w/ Test-Prep ExperienceExperienced Teacher and Education Profes...
4.9 4.9 (8 lesson ratings) (8)
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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