Question 381234
8 floors, 4 passengers. I will assume that the passengers begin at the first floor all going up, and any passenger gets off BEGINNING at the 2nd floor only (no one gets off at the 1st floor!)  We have to find the number of all ordered listings of four numbers out of seven, e.g., 2<3<7<8, 3<6<7<8, 4<5<6<8, etc.  That can be done in 7C4 ways.  The total numbers of ways 4 passengers can get off at 7 floors (starting at the 2nd!) is {{{7^4}}}.  Therefore the probability is {{{7C4/7^4 = 5/7^3 = 5/343}}}.