This sounds right to me.
8 people are in an elevator that goes up 6 floors. All 8 people exit the elevator by the 6th floor. The elevator operator is in the elevator watching them exit (the elevator operator does not count as one of the 8 people)
How many ways can the people exit the elevator if they are all identical?
This would just be
If there were 5 men and 3 women and the elevator operator could tell the men from women, how many ways could they exit the elevator?
Thus, # of ways to exit =
Now what if the elevator operator could distinguish each person (i.e. nobody is identical)
Would this just be
Thanks for any help!