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I am currently working on a personal project, and I've run into a dilemma.

I need to determine the total number of possible outcomes for a coin toss type system, ie two possible outcomes each generation, for N generations. The problem however comes in with the restrictions I have to deal with, these being.

1) Outcome one cannot occur x more times than outcome two.

2) Outcome two cannot occur y more times than outcome one.

Any "branch" of the probability tree that contains such a case needs to be eliminated.

I have no idea how to solve this, besides some form of excel type model with each branch manually calculated, but that looks terribly daunting when the system is allowed to run for many generations.

Any help would be appreciated.

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# Number of Possible Outcomes w/ Restrictions (Coin Toss)

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