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  1. Jan 27th, 2003, 11:16 AM #1
    bugzpodder
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    2 combinatorics questions

    Could someone find a proof other than induction for these two equations?

    1) nC1+2(n-1)*(nC2)+3(n-1)^2*(nC3)+...+n(n-1)^(n-1)*(nCn) = n^n

    where n in N and n >= 2

    2) Sum (from 3 to n) [3Pk*nCk] =(3Pn)*2^(n-3)



    by the way, 3Pk is k!/(k-3)! some ppl like to write kP3
    Last edited by bugzpodder; Jan 27th, 2003 at 11:21 AM.
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