Five people get on the elevator that stops at five floors. In how many ways they can get off? For example, one person gets off at the 1st floor, two will get off at the third, and the remaining two at the fifth floor. In how many ways they can get off at different floors? Now, consider that people in elevator have names, say A,B,C,D and E., assuming that, for example, the case A on the 1st floor is different from the case B on the 1st floor. Answer the previous questions with this assumption.
I was told that there are 4 questions, but I'm not really sure about it.
- People don't have names and get off
- People don't have names and get off at different floors
- People have names and get off
- People have names and get off at different floors.
Do the names matter?
I think I can answer one question out of 4 - the number of all outcomes should be $5^5=3125$. I am confused about the rest though