  We prove packing and counting theorems for arbitrarily oriented Hamilton
cycles in ${\cal D}(n,p)$ for nearly optimal $p$ (up to a $\log ^cn$ factor).
In particular, we show that given $t = (1-o(1))np$ Hamilton cycles $C_1,\ldots
,C_{t}$, each of which is oriented arbitrarily, a digraph $D \sim {\cal
D}(n,p)$ w.h.p. contains edge disjoint copies of $C_1,\ldots ,C_t$, provided
$p=\omega(\log ^3 n/n)$. We also show that given an arbitrarily oriented
$n$-vertex cycle $C$, a random digraph $D \sim {\cal D}(n,p)$ w.h.p. contains
$(1\pm o(1))n!p^n$ copies of $C$, provided $p \geq \log ^{1 + o(1)}n/n$.

Combinatorics