  The secretary and the prophet inequality problems are central to the field of
Stopping Theory. Recently, there has been a lot of work in generalizing these
models to multiple items because of their applications in mechanism design. The
most important of these generalizations are to matroids and to combinatorial
auctions (extends bipartite matching). Kleinberg-Weinberg \cite{KW-STOC12} and
Feldman et al. \cite{feldman2015combinatorial} show that for adversarial
arrival order of random variables the optimal prophet inequalities give a
$1/2$-approximation. For many settings, however, it's conceivable that the
arrival order is chosen uniformly at random, akin to the secretary problem. For
such a random arrival model, we improve upon the $1/2$-approximation and obtain
$(1-1/e)$-approximation prophet inequalities for both matroids and
combinatorial auctions. This also gives improvements to the results of Yan
\cite{yan2011mechanism} and Esfandiari et al. \cite{esfandiari2015prophet} who
worked in the special cases where we can fully control the arrival order or
when there is only a single item.
  Our techniques are threshold based. We convert our discrete problem into a
continuous setting and then give a generic template on how to dynamically
adjust these thresholds to lower bound the expected total welfare.
