  We prove an asymptotic formula for the number of partitions of $n$ into
distinct parts where the largest part is at most $t\sqrt{n}$ for fixed $t \in
\mathbb{R}$. Our method follows a probabilistic approach of Romik, who gave a
simpler proof of Szekeres' asymptotic formula for distinct parts partitions
when instead the number of parts is bounded by $t\sqrt{n}$. Although equivalent
to a circle method/saddle-point method calculation, the probabilistic approach
predicts the shape of the asymptotic formula, to some degree.
