c) $k(k-1) C_n^k = n(n-1) C_{n-2}^{k-2}$
Ta có
$VP = n(n-1) . \dfrac{(n-2)!}{(k-2)!(n-k)!}$
$= \dfrac{(n-2)!.n.(n-1)}{(k-2)! . k . (k-1) (n-k)!} . k(k-1)$
$= \dfrac{n!}{k!(n-k)!} . k(k-1)$
$= k(k-1) C_n^k = VT$
d) Áp dụng công thức ở Câu c) ta có
$VP = k(k-1) C_n^k + n . \dfrac{(n-1)!}{(k-1)! (n-k)!}$
$= k(k-1) C_n^k + \dfrac{n!}{k! (n-k)!}.k$
$= k(k-1) C_n^k + k.C_n^k$
$= C_n^k (k^2 - k + k)$
$= C_n^k . k^2 = VT$
