There are 9 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. How many different ways are there to schedule the appearance?

Question

mathmate · Answer

You can arrange 8 performers out of 8 in 8! ways.
There are 8 choices to choose from for the first performer,
7 for the second, 6 for the third,...until 1 for the 8th.
The 9th is already decided (if they all agreed).
So for n performers, there are n! ways.