If a restaurant offers 10 different toppings for its pizzas, and a customer chooses exactly 3 toppings for their pizza, how many possible topping combinations can the customer choose?
Instruction: Calculate the number of ways to choose 3 toppings out of 10 without regard to the order.
Context: This question assesses the candidate's understanding of combinations and their application in creating menu options.
Updated
Official answer
Choose three distinct toppings from ten, with order irrelevant. The count is C(10,3)=10×9×8/(3×2×1)=120.
The ordered count 720 lists each topping set six times, once for each ordering of its three members. Dividing by 3! removes that duplication. This assumes a topping is either present or absent; allowing repeated portions or different quantities would define another problem.