Question

Joe is ordering 3 hot dogs at Alpine City Beef. He can choose among five toppings for each hot dog: ketchup, mustard, relish, onions, and sauerkraut. In how many different ways can he choose 6 toppings?

a. 15 ways
b. 30 ways
c. 60 ways
d. 90 ways

Answer 1

Joe can choose 6 toppings for his three hot dogs in 5005 different ways.

Step-by-step explanation:

To find the number of different ways Joe can choose 6 toppings for his three hot dogs, we can use the concept of combinations. Since there are 5 toppings to choose from for each hot dog, there are 5 options for the first topping, 5 options for the second topping, and so on.

Therefore, the total number of ways Joe can choose the toppings is 5 * 5 * 5 = 125 ways. However, this counts each combination multiple times because the order in which the toppings are chosen doesn't matter.

Since Joe can choose 6 toppings, we have to divide the total number of ways by the number of possible arrangements of 6 toppings. This can be calculated using the combination formula:

C(n, r) = n! / (r! * (n-r)!)

Applying this formula, we get:

C(15, 6) = 15! / (6! * (15-6)!) = 15! / (6! * 9!)

Calculating this expression, we find that Joe can choose 6 toppings in 5005 different ways.