Prove Pascals Formula by using the fact that nCk = n!/(k!(n-k)!)

Prove that k*(nCk) = n*(n-1)C(k-1) by using the same fact from above.

Use the lattice walk idea to prove that nCk = nC(n-k).

Use the lattice walk idea to prove nC0 + nC1 + ... + nCn = 2^n

If anyone can show any of these, I would greatly appreciate it. Thanks!