Question

There are performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last standup comic of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances?

Answer 1

We have to use basic combinatorics to solver his problem. We first have to determine what kind of problem this is. 

Does order matter in this question? Yes it does. So it is a permutation. 

Is is a permutation with repetition? No, because once a performer goes, they cannot perform again. Hence, we have defined this problem as a permutation without repetition.BUT HOW MANY PERFORMERS ARE THERE??