Combinations and Permutations in Pizzas

The video tutorial explains how to calculate the number of possible three-topping pizzas using combinations, considering 12 available toppings. It then explores how to determine the total number of pizzas possible with any number of toppings from 0 to 12, using binary choices for each topping. Finally, it discusses permutations to arrange toppings in two columns on a menu, emphasizing the importance of order in permutations.

How many different three-topping pizzas can be made from 12 toppings?

• 220

• 320

• 420

• 120

What mathematical concept is used to determine the number of three-topping pizzas?

• Factorial

• Probability

• Combination

• Permutation

What is the formula for calculating combinations?

• n! / (n-k)!

• n! / (k!(n-k)!)

• k! / (n-k)!

• n! / k!

How many total pizzas can be made with 0 to 12 toppings?

• 4096

• 2048

• 1024

• 8192

What is the faster method to calculate the total number of pizzas with 0 to 12 toppings?

• Using factorials

• Using powers of 2

• Using combinations

• Using permutations

How many choices are there for each topping when calculating total pizzas with 0 to 12 toppings?

• Four

• Two

• One

• Three

How many toppings are placed in each column when arranging 12 toppings into two columns?

• Four

• Five

• Seven

• Six

What mathematical concept is used to arrange toppings in one column?

• Combination

• Statistics

• Permutation

• Probability

What is the formula for calculating permutations?

• n! / (k!(n-k)!)

• k! / (n-k)!

• n! / k!

• n! / (n-k)!

How many ways can the six toppings in the left column be arranged?

• 700,000

• 600,000

• 720,000

• 665,280