Finite MAth

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Assume that the set S has 7 elements.
How many subsets of S have at most 3 elements

  • Finite MAth -

    The total number of subsets = 2^7 = 128
    This includes the null set

    So what we want is
    the null set, the set of singles, the set of doubles and the set of triples
    = 1 + C(7,1) + C(7,2) + c(7,3)
    = 1 + 7 + 21 + 35
    = 64

    So the number of subsets with at most 3 elements is 64

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