Captain Jessica has a ship, the H. M.S. Khan. The ship is two furlongs from the dread pirate Luis and his merciless band of thieves. The Captain has probability 4/9 of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability 1/4 .If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?

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."