Question

The Futurists, a rock group, are planning a concert tour with performances to be

given in five cities: San Francisco, Los Angeles, San Diego, Denver, and Las Vegas.
how many ways can they arrange their itinerary if

a.There are no restrictions?

b.The tree performances in California must be given consecutively?​

Answer 1

a. 24

b. 12

Explanation:

a. You can choose from 4 cities for the first performance, then from 3 cities, then from 2 cities, then the last city.

4 * 3 * 2 * 1 = 24

b. Think of the three performances in California as a unit. Within this unit, you can choose from 3 cities for the first one, then 2 cities for the second one, and finally 1 city for the last one.

3 * 2 * 1 = 6

Now you can have the 3 California performances first, followed by Denver, or Denver first followed by California.

6 * 2 = 12