Expressions are developed which describe the ensemble average of the annihilation of groups of contiguous vacant compartments when spatially random attempts are made to place dumbbells on a linear array of N
compartments. It is shown that in the limit, as the number of compartments tends to infinity, <θp
)>, the ensemble average of the fraction of the compartments which is composed of p
contiguous vacant compartments, is given by
is the striking frequency of the dumbbells, t
is time, and the Cn
's are appropriately defined coefficients.