how would I prove that an equation involving combinations are equal?

k*C(n+1,k) = (n+1)*C(n,k-1)

I need to prove this equality. Any ideas? No need for exact answers, just a general direction would help. Thanks

1 Answer

Relevance
  • pki15
    Lv 4
    1 decade ago
    Favorite Answer

    k*C(n+1,k)

    = k * (n+1)!/(k!(n+1-k)!)

    = (n+1)!/((k-1)!(n+1-k)!)

    = (n+1) * n!/((k-1)!(n+1-k)!)

    = (n+1) * C(n, k-1)

Still have questions? Get your answers by asking now.