# Thread: Combinatorial and algebraic proof involving a permutation

1. ## Combinatorial and algebraic proof involving a permutation

Hi guys, can anyone please tell me the combinatorial and algbraic proof of P(n+1, r) = P(n,r) + P(n,r-1)? Thanks for your help.

2. No.

What are you even talking about?

That is not true of permutations. Let $\displaystyle n=10~\&~r=4$
$\displaystyle \mathcal{P}(n+1,r)=7920$ while $\displaystyle \mathcal{P}(n,r)+\mathcal{P}(n,r-1)=5760$
Is true for combinations $\displaystyle \mathcal{C}(n+1,r)= \mathcal{C}(n,r)+ \mathcal{C}(n,r-1)$.