Question

(a) There are European cities that Betty would eventually like to visit. On her next vacation, though, she only has time to visit of the cities: one on Monday, one on Tuesday, and one on Wednesday. She is now trying to make a schedule of which city she'll visit on which day. How many different schedules are possible

Answer 1

The number of different schedules possible is given by:

`P_((n,3)) = (n!)/((n-3)!)`

In which n is the number of European cities that Betty would eventually like to visit.

Explanation:

The order in which the cities are visited is important, for example, visiting Paris on Monday and London on Tuesday is a different schedule than London on Monday and Paris on Tuesday. This means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

She wants to visit n cities on 3 days:

So the number of different schedules possible is given by:

`P_((n,3)) = (n!)/((n-3)!)`

In which n is the number of European cities that Betty would eventually like to visit.