Combinations and Factorials in Pizzas

The video tutorial explains how to determine the number of possible four-topping pizzas from a choice of fourteen toppings. It discusses the difference between permutations and combinations, emphasizing that order does not matter in this scenario, thus using combinations. The tutorial walks through the combination formula, simplifying it step-by-step, and verifies the result using a calculator, concluding that there are 1,001 possible combinations.

How many different toppings does the pizza parlor offer?

• Ten

• Twelve

• Sixteen

• Fourteen

What mathematical concept is used when the order of selection does not matter?

• Multiplication

• Division

• Combination

• Permutation

In the context of the problem, why is a combination used instead of a permutation?

• Because the order of toppings changes the pizza

• Because the order of toppings does not change the pizza

• Because there are more than ten toppings

• Because permutations are more complex

What is the value of n in the combination formula for this problem?

• Four

• Ten

• Fourteen

• Twenty

What is the factorial of four (4!)?

• 12

• 16

• 32

• 24

Which of the following is a step in simplifying the combination formula?

• Multiplying all terms by two

• Cancelling out common factors

• Adding all terms together

• Subtracting the smaller factorial from the larger one

What is the result of the combination calculation for the number of four-topping pizzas?

• 500

• 1500

• 1001

• 750

What is the first step in using a calculator to verify the combination?

• Press the addition button

• Enter the number of pizzas

• Enter the number of toppings

• Select the permutation option

Which calculator function is used to find combinations?

• Division

• Addition

• Subtraction

• Probability

What is the final number of possible four-topping pizzas?

• 1001

• 1500

• 500

• 100