  Certain biochemical reactions can only be triggered after binding of a
sufficient number of particles to a specific target region such as an enzyme or
a protein sensor. We investigate the distribution of the reaction time, i.e.,
the first instance when all independently diffusing particles are bound to the
target. When each particle binds irreversibly, this is equivalent to the
first-passage time of the slowest (last) particle. In turn, reversible binding
to the target renders the problem much more challenging and drastically changes
the distribution of the reaction time. We derive the exact solution of this
problem and investigate the short-time and long-time asymptotic behaviors of
the reaction time probability density. We also analyze how the mean reaction
time depends on the unbinding rate and the number of particles. Our exact and
asymptotic solutions are compared to Monte Carlo simulations.
