1. The problem statement, all variables and given/known data I am trying to come up with a logical explanation (using an example from real life modeled in Combination and/or Permutation) to show that 3^n = summation (from i=0 to n) of (n choose i)*(2^i). In other words, I am trying to pose a combinatorial/selection/combination question that then can be modeled as both sides of the equation. 2. Relevant equations Combinations and Permutations. 3. The attempt at a solution My trial is that 3^n could be modeled as having 3 boxes and we are placing n items in it (eg. balls). So, if we pick n=5, it is as selecting 3 balls to put in box one, then returning them, then selecting 3 balls to put in box 2, then returning..etc while the order of selection is "don't care". However, I still can't show how that translates into the right side of the equation. Any help or pointers?