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Combinatorial Identities Table I Intermediate Form

Combinatorial Identities Table I Intermediate Form

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last time on mastering AMC 1012 we covered stars and bars and some very interesting examples but today we're covering combinatorial identities starting off with the binomial identity this basically states that N20 percent choose one all the way till plus n choose n is 2 to the n now why is this true well you can think about n objects so if we have n objects the number of ways of selecting zero objects is then choose zero the number of ways of choosing one object is then choose one the number of ways of choosing two objects is entries two so on all the way until the number of ways of choosing n objects is n choose n we can also count this by noticing that for each object we have two choices it's either we count it or we don't so we use a combinatorical proof of this identity to see where this actually comes from and it's very powerful and it's very useful in many different AMC and even Beyond so Vander money's identity now this is extremely powerful because it allows you to convert this

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