Show that `(n+1)(""^(n)P_(r)) = (n-r+1)[""^(n+1)P_(r)]`

Show that : (n !) / (r ! (n - r) !) + (n !) / ((r - 1) ! (n - r + 1) !) = ((n + 1) !) / (r ! (n - r +1) !)

Find x if ^(n)P_r = x ^(n)C_r

Find n if, ^(2n)C_(r-1) = ^(2n)C_(r+1)