I can prove these algebraically with no problems but I'm having trouble explaining with words why they are true i.e. with acombinatorial argument. Can someone give me a hint?

$\displaystyle C(n, k) = C(n-2, k-2) + 2C(n-2, k-1) + C(n-2, k)$

$\displaystyle P(n, k) = P(n-1, k) + kP(n-1, k-1)$

Thank you.