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binomial coefficients n choose k are how we count the number of ways to choose k objects out of n clearly that must mean that n must be positive right we can choose three objects out of a total of five but how would we choose three objects out of a total of negative five what does that even mean and even if we could make sense of it why would we care here is the set of positive integers up to n which we will denote as n in brackets from this set we can make various classes of combinatorial objects such as a class of all subsets of n with three elements how many objects are in this combinatorial class letamp;#39;s write a function f of n to represent it in this case we merely choose three out of the n integers from the set so the number of objects in this class is just n choose 3. hereamp;#39;s a question for you to ponder what is the domain of this function in other words what values of n are allowed to be plugged into this function in this form most people would very reasona
