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I have two balls: {A, B} and 3 slots.

  • Each slot can contain one of the balls
  • Balls can repeat, e.g. {A, A, B} is ok
  • Order matters, e.g. {A, A, B} is not the same as {B, A, A}

I want to know the number of combinations that do not contain at least one A and one B.

So for the above case, the answer is 2: {A, A, A} and {B, B, B}.

I need this question answered in the general case: I have X distinct balls, and Y slot, for Y > X. Given the total number of combinations, how many combinations do not contain each of the X balls.

Thank you.

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    I think you are doing great so far..just advance to three balls (A, B and C) and 4 slots (and then to 5 slots)2012-10-31

1 Answers 1