Can't do combinatorial proofs. Can someone help?

• October 20th 2009, 09:22 AM
babbagandu
Can't do combinatorial proofs. Can someone help?
Sorry I don't know how to type this in mathematical symbols.
Prove that:

the summation from r=0 to n of (C(n,r))(a-1)^r = a^n

Thanks for any help I can get
• October 20th 2009, 09:39 AM
Plato
Use the binomial theorem.
$\left( {x + y} \right)^n = \sum\limits_{r = 0}^n {\binom{n}{r}x^r y^{n - r} }$

Let $x=(a-1)~\&~y=1$