How many ways can Marie choose 3 pizza toppings from a menu of 17 toppings if each topping can only be chosen once? Answer How to enter your answer (opens in new window)

Step 1 ：This problem is about combinations. In combinatorics, a combination is a selection of items without considering the order. Since the order in which the pizza toppings are chosen does not matter, we can use the combination formula to solve this problem.

Step 2 ：The combination formula is given by: \(C(n, k) = \frac{n!}{k!(n-k)!}\) where: n is the total number of items, k is the number of items to choose, and '!' denotes factorial, which is the product of all positive integers up to that number.

Step 3 ：In this case, n = 17 (the total number of pizza toppings) and k = 3 (the number of toppings to choose).

Step 4 ：Substituting the given values into the combination formula, we get \(C(17, 3) = \frac{17!}{3!(17-3)!}\)

Step 5 ：Solving this, we find that there are 680 ways for Marie to choose 3 pizza toppings from a menu of 17 toppings.

Step 6 ：Final Answer: \(\boxed{680}\)