In mathematics, Pascal's rule is a combinatorial identity about binomial coefficients. It states that for any natural number n we have
where
is a binomial coefficient. This is also commonly written
When X is not in the subset, you need to choose all the k elements in the subset from the n − 1 objects that are not X. This can be done in
ways.
We conclude that the numbers of ways to get a k-subset from the n-set, which we know is
, is also the number 
See also Bijective proof.
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