Combinations and Toppings Selection

The video tutorial explains how to calculate the number of ways to choose four distinct toppings from a list of 10 vegetarian options using combinations. It covers scenarios where pineapple is excluded or included as a topping, demonstrating the calculations for each case. The tutorial uses factorials and simplification techniques to find the number of possible combinations, providing a clear understanding of the mathematical concepts involved.

What mathematical concept is used to determine the number of ways to choose pizza toppings?

• Permutation

• Combination

• Probability

• Statistics

How many vegetarian toppings are available to choose from?

• 11

• 10

• 9

• 8

What is the formula for calculating combinations?

• n! * k!

• n! / (n-k)!

• n! / k!

• n! / [(n-k)! * k!]

What is the result of 10 choose 4?

• 120

• 210

• 252

• 302

What is the first step in simplifying 10 choose 4?

• Expand 4 factorial

• Multiply by 4 factorial

• Expand 10 factorial

• Divide by 6 factorial

If pineapple is not included, how many toppings are available?

• 10

• 7

• 8

• 9

What is the result of 9 choose 4?

• 84

• 126

• 210

• 252

If pineapple is included, how many additional toppings need to be chosen?

• 5

• 3

• 4

• 2

What is the result of 9 choose 3?

• 72

• 84

• 96

• 56

What is the common factor used to simplify 9 and 3 in the calculation?

• 2

• 3

• 5

• 4