There are 4 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic of the evening. If this performer’s request is granted, how many different way are there to schedule the appearances?
Since one performer has demanded to be the last act of the evening, you only have three performers to schedule for the other sport. If a performer is chosen to be the first act, this leaves two choices for the second act.
Of the two performers left, choose one to be the second act at the comedy club. This leaves one choice for the third act.
Recall that the last act’s performer has already been chosen, so there is only one choice for the last act.
Use the Fundamental Counting Principle to find the number of ways you can schedule the appearances of the four performers. Multiply the choices:
3 * 2 * 1 * 1 = 6 ways
Thus, you can arrange the performers in 6 ways. There are 6 different possible permutations.