# Math Help - People Exiting an Elevator

1. ## People Exiting an Elevator

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 $\binom{6+8-1}{6-1} = \binom{13}{5}$

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?

Men = $\binom{5+6-1}{6-1} = \binom{10}{5}$

Women = $\binom{3+6-1}{6-1} = \binom{8}{5}$

Thus, # of ways to exit = $\binom{10}{5} * \binom{8}{5}$

Now what if the elevator operator could distinguish each person (i.e. nobody is identical)

Would this just be $6^8$

Thanks for any help!

2. ## Re: People Exiting an Elevator

This sounds right to me.