Combinatorial Proof Help?

Prove that:

C(n+k)C(n,k) = C(n+k,n-k)C(2k,k)

Update:

That should be for C(n+k,k)

2 Answers

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  • kb
    Lv 7
    6 years ago
    Favorite Answer

    Simply use the definition of the binomial coefficient, and rearrange factors as necessary.

    C(n+k, k) C(n, k)

    = ((n+k)!/(k! n!)) * (n!/(k! (n-k)!))

    = (n+k)!/(k! k! (n-k)!)

    = ((n+k)!/((n-k)! (2k)!)) * ((2k)!/(k! k!))

    = C(n+k, n-k) C(2k, k).

    I hope this helps!

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  • Tomp
    Lv 7
    6 years ago

    The first factor is missing a parameter.

    • I am6 years agoReport

      That should be for C(n+k,k)

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