A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 13 feet per second. One day, the equipment elevator begins to descend. After 24 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 14 seconds? At that time, which elevator is deeper?

what

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."