20 balls

How many ways can we arrange 10 identical black balls and 10 identical red balls in a line, so that no ball has two neighbors that are of the same color?

Clarification: No ball (red or black) can be between two black balls or two red balls.

So, the following combinations aren't allowed for any three successive balls:

  • BRB
  • BBB
  • RRR
  • RBR

Image credit: https://www.dreamstime.com


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