Question

Suppose that 5 customers arrive, and each orders a different appetizer to share from a choice of 12 appetizers. In how many ways can this be done?

Answer 1

The number of ways to choose a different appetizer for each of the 5 customers from a choice of 12 appetizers is 95,040.

Step-by-step explanation:

The number of ways to choose a different appetizer for each of the 5 customers from a choice of 12 appetizers can be calculated using permutations. In this case, the order in which the appetizers are chosen does matter, and repetition is not allowed since each customer must choose a different appetizer.

To calculate the number of ways, we can use the formula for permutations:

P(n, r) = n! / (n-r)!

Where n is the total number of items and r is the number of items to be chosen.

So, in this case, the number of ways to choose the appetizers is:

P(12, 5) = 12! / (12-5)! = 12! / 7!

Using a calculator simplifies to:

P(12, 5) = 95,040

Answer 2

2 ways with a remainder of 2