Question

At Pizza Hut, a customer wants to buy some pizza. How many different ways can a customer buy 4 different types of pizzas out of 11?

a. For this example, what formula will we need to use?

Permutation : n P r = n ! ( n − r ) !

Perumtation Rule #2 : n ! r 1 ! ⋅ r 2 ! ⋅ r 3 ! ⋅ ... ⋅ r p !

Fundamental Counting Rule : k 1 ⋅ k 2 ⋅ k 3 ⋅ ... ⋅ k n

Combination : n C r = n ! ( n − r ) ! ⋅ r !

b. Please explain how we know we are supposed to use that formula. We are picking from multiple groups (or categories) and within each group have different choices. We are picking from one group multiple times and order matters. We are rearranging all the items that come from multiple groups (or categories) and within each group there are identical items (repeats). We are picking from one group multiple times and order does not matter.

c. How many different ways can a customer buy 4 different types of pizzas out of 11? (Do work on a separate piece of paper) There are different ways a customer can buy 4 pizzas out of 11 choices.

Answer 1

Let the eleven different pizzas on the menu be denoted by

The order does not matter since     or or any other arrangement are equivalent and means that the customer has bought the first four pizzas on the list.

The formula is the combination formula:

The reason is that we are picking from one group multiple times and the order does not matter.

The number of ways is: