If the band plays 5 cities in total, how many different concert schedules can be formed if there is no restriction in which cities they play?A rock band is planning a tour of BC. They intend on...

If the band plays 5 cities in total, how many different concert schedules can be formed if there is no restriction in which cities they play?

A rock band is planning a tour of BC. They intend on playing on some of 12 cities.

mlehuzzah | Student, Graduate | (Level 1) Associate Educator

Posted on

By "no restriction" I am assuming the band can play in the same city multiple times, even leaving, playing elsewhere, and then returning to that city.

So, the band will play 5 shows.  Each show they have 12 different cities in which they can play.  The number of such concert schedules is 12*12*12*12*12 = 248832

Now, if the band can't return to a city once they have played there, then for their first show, they have 12 choices for the show.  But after they play their first show, say in Vancouver, they only have 11 possible city choices for their second show (the 12 cities minus Vancouver).  After they play their second show, say in Victoria, they only have 10 possible choices for their third show.  The number of possible concert schedules is:

12*11*10*9*8=95040