Use the Combinations Formula
-A hamburger shop sells hamburgers with cheese, relish, lettuce, tomato, onion, mustard, or ketchup. How many different hamburgers can be concocted using any 3 of the extras?
A) 35
B) 210
C) 840
D) 105

Question

Quizplus · Accepted Answer

The combinations formula is used to find the number of ways to choose k items from n items without regard to the order of selection. The formula is C(n, k) = n! / [k!(n-k)!]. Here, n = 7 (cheese, relish, lettuce, tomato, onion, mustard, ketchup) and k = 3. Thus, C(7, 3) = 7! / [3!(7-3)!] = 7! / (3!4!) = (7×6×5) / (3×2×1) = 35.