How many different groups of students can show up for a seminar with an enrollment of 11 ?

For this question, will we use permutations.

So, how many people can be in the first group? 11. Then what about the second group? Well because there is already at least one person in the slot for the group it must 10. Then so on.

Then we multiply all of the terms.

11*10*9*8*7*6*5*4*3*2*1 or 11! Which means the same thing.

11! = 39916800

There are 39916800 ways to make a group.