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Permutations And CombinationsInduction

# Permutations And CombinationsInduction - 1 Permutations And...

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1 Permutations And Combinations: Proof by Induction We have the relation expressed by the arrows can be written mathematically as: 1 1 n n n k k k We could also derive this formula by considering the definition of “n choose k” as the number of subsets. When we have n+1 items to choose from, we can pick out one of the items, call it A, and then say: every subset having exactly k items either does contain A, or does not contain A. If it does not contain A, then it is one of the subsets that contains k items, and is drawn from the set of exactly n items that we have when we do not contain A. There are exactly n k of these subsets. OR, it does contain the element A. It must also have 1 k other elements, and they must be drawn from the 1 n other elements in the set. So the number of such subsets (the ones that do contain A) is exactly 1 n k . The subsets that we count

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Permutations And CombinationsInduction - 1 Permutations And...

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