Solve the problem.
-A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 3 of the extras?
A)105
B)35
C)840
D)210

Question

Quizplus · Accepted Answer

The problem can be solved using combinations since the order of the toppings does not matter. The formula for combinations is nCr = n! / [r!(n-r)!], where n is the total number of items to choose from, r is the number of items to choose, "!" denotes factorial, which is the product of all positive integers up to that number. Here, n=7 (cheese, relish, chili, tomato, onion, mustard, ketchup) and r=3 (choosing any 3 of the extras). So, 7C3 = 7! / [3!(7-3)!] = 7! / (3!4!) = (7x6x5) / (3x2x1) = 35.

Solve the Problem. -A Hot Dog Stand Sells Hot Dogs with Cheese, Relish