Eight people enter a subway train and must exit at four stations, with at least one person exiting at each station. The problem asks to calculate the number of ways this can occur. The solution is that there are 8 choices for the first exit, 7 for the second, 6 for the third, and 5 for the fourth. Multiplying these choices gives 1680 ways for 4 people to exit over 4 stations. Since the remaining 4 people can exit at any station, the total number of ways is 1680 * 4 * 4 * 4 * 4 = 430080.
4 people exit subway train at 4 stations in 1680*4^4 ways
1. Eight people enter a subway train at a given station. At least one of these eight passengers exits
the train at each of the next four stations. The fourth station is the end of the line and all
remaining passengers must depart. How many ways can this happen?
Solution
4 people exists at the stations
no of ways to do this is 8C1 * 7C1 * 6C1 *5C1 = 8*7*6*5 = 1680
now there are 4 passengers are left
they have t exit at any of the four stations
so each passenger can exit the train in 4 ways
so total no of ways = 1680*4*4*4*4 = 430080
