The assignment of n facilities to n locations, with the objective of minimizing the total cost of the design, is known as the facilities design problem. For a problem of size 𝓃, there are 𝓃! feasible solutions, which can be represented by a frequency distribution of total costs. Recent statistical analyses have indicated that these distributions can be adequately described as gamma, and for many practical purposes the log normal or normal distributions give good approximations. The absolute mean of all the 𝓃!assignments can be easily calculated.