I'm trying to give combinatorial (not algebraic!) proofs of the following statements:

(1) P_r^{n+1}=r!+r(P_{r-1}^n+P_{r-1}^{n-1}+...+P_{r-1}^r)

(2) P_r^n=\frac{n}{n-r}P_r^{n-1}

where P_r^n denotes the number of r-permutations of elements from an n-element set. In other words, if we have an n-element set A=\{x_1,...,x_n\} then one r-permutation would be an ordered r-tuple of different elements from A, i.e. (x_1,...,x_r), such that x_i \in A, x_i \neq x_j whenever i \neq j.

Any help would be greatly appreciated!