
arrangements help
Prove from the defintion of nPr (as in nPr = n!/(nr)!) that
(n+1)/Pr = nPr + r.nP(r1)
and show that nPr = (n2)Pr + 2r. (n2)P(r1) + r(r1) x (n2)P(r2)
if anyone could give me some techniques or some help solving these types of questions i would really appreciate it ! thankyou =D

$\displaystyle P_n^r+rP_n^{r1}=\frac{n!}{(nr)!}+r\cdot\frac{n!}{(nr+1)!}=$
$\displaystyle =\frac{n!(nr+1)}{(nr+1)!}+\frac{n!r}{(nr+1)!}=\frac{n!(nr+1+r)}{(nr+1)!}=\frac{(n+1)!}{(nr+1)!}=P_{n+1}^r$
Now we use this formula to prove the second identity.
$\displaystyle P_n^r=P_{n1}^r+rP_{n1}^{r1}=P_{n2}^r+rP_{n2}^{r1}+r(P_{n2}^{r1}+(r1)P_{n2}^{r2})=$
$\displaystyle =P_{n2}^r+2rP_{n2}^{r1}+r(r1)P_{n2}^{r2}$

thanx so much for your help !