  Based on early solar system abundances of short-lived radionuclides (SRs),
such as $^{26}$Al (T$_{1/2} = 0.74$ Myr) and $^{60}$Fe (T$_{1/2} = 1.5$ Myr),
it is often asserted that the Sun was born in a large stellar cluster, where a
massive star contaminated the protoplanetary disk with freshly
nucleosynthesized isotopes from its supernova (SN) explosion. To account for
the inferred initial solar system abundances of short-lived radionuclides, this
supernova had to be close ($\sim$ 0.3 pc) to the young ($\leqslant$ 1 Myr)
protoplanetary disk.
  Here we show that massive star evolution timescales are too long, compared to
typical timescales of star formation in embedded clusters, for them to explode
as supernovae within the lifetimes of nearby disks. This is especially true in
an Orion Nebular Cluster (ONC)-type of setting, where the most massive star
will explode as a supernova $\sim$ 5 Myr after the onset of star formation,
when nearby disks will have already suffered substantial photoevaporation
and/or formed large planetesimals.
  We quantify the probability for {\it any} protoplanetary disk to receive SRs
from a nearby supernova at the level observed in the early solar system. Key
constraints on our estimate are: (1) SRs have to be injected into a newly
formed ($\leqslant$ 1 Myr) disk, (2) the disk has to survive UV
photoevaporation, and (3) the protoplanetary disk must be situated in an
enrichment zone permitting SR injection at the solar system level without disk
disruption. The probability of protoplanetary disk contamination by a supernova
ejecta is, in the most favorable case, 3 $\times$ 10$^{-3}$.
