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

Question

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

 

Answer 1

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

Answer 2

Because order is important, this is a permutation. The formula for permutation _nP_k  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!.

Answer 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.

Answer 4

It can be done in 7!/((3!)*(4!)) =35 ways

 

Jim