On a TV game show, a contestant is shown 9 products from a grocery store and is asked to choose the three least-expensive items in the set. The three chosen items need not be in any particular order. In how many ways can the contestant choose the three items?
A)6
B)504
C)60,480
D)84

Question

Quizplus · Accepted Answer

The contestant is choosing 3 items out of 9 without regard to the order, which is a combination problem. The number of ways to choose 3 items from 9 is calculated using the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items to choose from (9 in this case), k is the number of items to choose (3 in this case), and "!" denotes factorial, the product of all positive integers up to that number. Therefore, C(9, 3) = 9! / [3!(9-3)!] = 9! / (3!6!) = (9*8*7) / (3*2*1) = 84.

On a TV Game Show, a Contestant Is Shown 9