Part A) only
Show that for integers k and n such that `1<=k<=n` ,
`k^nC_k = n ^(n-1)C_(k-1)`
Hence or otherwise prove that for any `x in RR` and n>=0,
`sum_(k=0)^n k^nC_kx^k (1-x)^n-k = nx`
`= k(n!)/(k!(n-k)!) `
So the answer is proved as required.