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?
A) 5,040
B) 840
C) 420
D) 210

Question

Quizplus · Accepted Answer

This is a permutation problem because the order in which the locations are ranked matters. The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. Here, n = 7 (locations) and r = 3 (top three locations). Thus, P(7, 3) = 7! / (7-3)! = 7! / 4! = (7*6*5*4!) / 4! = 7*6*5 = 210.

A Business Has Seven Locations to Choose from and Wishes