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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).

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?

Thanks!

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# Modeling a power as sum of combination

Can you offer guidance or do you also need help?

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