This is for a discrete mathematics course There are 18 fish

This is for a discrete mathematics course:

There are 18 fish and 4 aquariums. How many different possibilites are there to seperate the fish into the aquariums, assuming that each aquarium must have at least 1 fish?

Solution

Place the 8 apples in a row with gaps between then. See diagram below. * * | * | * * * * | * To separates 18 fish into 4 aquarium we must choose 3 separators \'|\' to place in the gaps. There are 17 gaps and we must choose 3 from amongst the 17. This can be done in C(17,3) = 680 ways