How many ways are there to put 5 balls in 2 boxes if the balls are distinguishable and the boxes are distinguishable?

Guest Jun 24, 2019

#1**+2 **

When we have k distinguishable balls and n distinguishable boxes....and assuming that either box might be empty....then the number of ways to distribute the balls is given by :

n^{k} = (2)^{5} = 32 ways

When you think about it....if we looked at only Box1, each consignment of balls in this box would just be a subset of the number of total subsets formed by 5 objects in a set = 2^{5}

CPhill Jun 24, 2019