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Summing the Multinomial Coefficients
The sum of binomial coefficients equals 2n, because is the number of ways to pick j elements from a set of size n, and 2n is the size of the powerset, the set of all subsets, of a set of size n: the...
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Inclusion, Exclusion
In this modern day and age, it simply cannot be doubted that it is of the very utmost importance that we find the size of the union of some sets. One might try just adding the sizes of all the sets,...
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Computing the Powerset
Suppose we want to find the powerset of a given set, that is, the set of all its subsets. How might we go about it? Well, the powerset of the empty set is the set containing the empty set. And the...
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