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Simplify the alternating sum using the Binomial Theorem n 0 n 1 3 n 2...

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Simplify the alternating sum using the Binomial Theorem n 0 n 1 3 n 2 9 n 3 27 cdots 1 n n n 3 n A store sells 4 different kinds of T shirts of your size a In how many different ways can you buy ten T shirts b How many different combinations of ten T shirts will have at least one of each kind

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