Supp#3COMBINATORICS_AND_PROBABILITY_DISTRIBUTIONS

# Supp#3COMBINATORICS_AND_PROBABILITY_DISTRIBUTIONS - EE 150...

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1 EE 150 COMBINATORICS AND PROBABILITY DISTRIBUTIONS We have shown that the number of subsets of k objects that can be wrought from an original group of n objects [the order in which the objects are placed in each subset being unimportant] is: C(n,k) = [Equation one] This formula presents itself in many situations. Imagine that you toss a coin five times and you want the number of ways that you can toss two heads in five tosses. Tossing a head on the first and fourth toss represents a unique subset of two taken out of an original group of five. So the number of ways of tossing two heads in five tosses is simple C(5,2) . Remarkably if you expand a binomial to some power the coefficients in the expansion are given by the combination formula in particular: n ( x+y) n = Σ [ n ! / k ( n – k ) ] x k y n - k k=0 [Equation two]

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