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math

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Why does 0!=1

  • math - ,

    here is a rather simple explanation

    we know n! = n(n-1)!
    e.g. 6! = 6(5!)

    and 1! = 1(0!) and we know that 1! = 1
    so 1 = 1(0!)
    0! = 1

    another way is to look at the definition of C(n,r) which are the number of subsets of n elements.
    e.g. C(6,2) is the number of 2-element subsets in 6 elements, and C(6,2) = 6!/(4!2!) = 15

    so C(6,0) would be the number of null subsets, which of course is 1.
    there is one null subset.

    but C(6,0) = 6!/(6!0!)
    720 = 720/(720(0!))
    so 0! has to be 1

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