Question

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

Answer 1

Answer: 210

Step-by-step explanation:

Given: total locations = 7

Number of locations wishes to rank = 3

If order of selection matters, then the number of permutations of r things from n= $\dfrac{n!}{(n-r)!}$

The number of ways to rank 3 locations out of 7 $=\dfrac{7!}{(7-3)!}=7\times6\times5=210$

Hence, the number of different ways required = 210