1. ## arrangements help

Prove from the defintion of nPr (as in nPr = n!/(n-r)!) that
(n+1)/Pr = nPr + r.nP(r-1)
and show that nPr = (n-2)Pr + 2r. (n-2)P(r-1) + r(r-1) x (n-2)P(r-2)

if anyone could give me some techniques or some help solving these types of questions i would really appreciate it ! thankyou =D

2. $P_n^r+rP_n^{r-1}=\frac{n!}{(n-r)!}+r\cdot\frac{n!}{(n-r+1)!}=$

$=\frac{n!(n-r+1)}{(n-r+1)!}+\frac{n!r}{(n-r+1)!}=\frac{n!(n-r+1+r)}{(n-r+1)!}=\frac{(n+1)!}{(n-r+1)!}=P_{n+1}^r$

Now we use this formula to prove the second identity.

$P_n^r=P_{n-1}^r+rP_{n-1}^{r-1}=P_{n-2}^r+rP_{n-2}^{r-1}+r(P_{n-2}^{r-1}+(r-1)P_{n-2}^{r-2})=$

$=P_{n-2}^r+2rP_{n-2}^{r-1}+r(r-1)P_{n-2}^{r-2}$

3. thanx so much for your help !