In how many ways can you distribute 18 fruits among 18 pirates so that each gets 1 piece of fruit? > Assume you have 5 oranges, 7 limes, and 6 lemons. How many ways can you distribute these among 18 pirates so they can each get 1 fruit and avoid scurvy? (This is a **homework** problem) My first instinct is: $18^{18}$, but that didn't seem right. My next thought was: $18!$. The problem doesn't specifically state whether or not repetition counts, so I am not sure what to assume. For instance, if Pirate A gets an orange, does that count for each other orange he could be given?

Not 18 factorial..

When you are arranging items (basically what we're doing here) you have to divide by how many ways each subset of identical items can be arranged. In this case, there are $18!$ ways to hand out the fruit, but how many ways can you arrange the oranges, limes, and lemons?