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Inclusion Exclusion Core Form

Inclusion Exclusion Core Form

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welcome back to discret mathematics today we're going to look at the inclusion Exclusion Principle but mainly exactly and at least M conditions so we're going to use the S notation so s0 means zero elements or zero conditions satisfying S1 means the number of elements Satisfied by EXA or one condition so well I'm going to give you the formulas and then we'll talk a little bit about how we can derive them but not that important so exactly m is going to be S minus m + 1 choose 1 s m + 1 plus m + 2 choose 2 s m + 2 and that's just going to keep alternating on and on until you hit the last condition so the top and the bottom for these chooses are just going up by one if that helps you learn this a little bit easier uh the least M conditions are very similar so we start out with s then we subtract M choose 1 SM + 1 then we add m + 1 choose 2 SM + 2 and this just goes on and on just like the first one so it follows the same pattern except this m here i

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