  Suppose that $N_0$ independently diffusing particles, each with diffusivity
$D$, are initially released at $x=\ell>0$ on the semi-infinite interval $0\leq
x<\infty$ with an absorber at $x=0$. We determine the probability ${\cal P}(N)$
that $N$ particles survive until time $t=T$. We also employ macroscopic
fluctuation theory to find the most likely history of the system, conditional
on there being exactly $N$ survivors at time $t=T$. Depending on the basic
parameter $\ell/\sqrt{4DT}$, very different histories can contribute to the
extreme cases of $N=N_0$ (all particles survive) and $N=0$ (no survivors). For
large values of $\ell/\sqrt{4DT}$, the leading contribution to ${\cal P}(N=0)$
comes from an effective point-like quasiparticle that contains all the $N_0$
particles and moves ballistically toward the absorber until absorption occurs.
