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A study examined the feasibility of developing a cost effective sampling technique which would estimate the mean number of patrons using the Purdue University General Library during one semester. The technique employed, called random sampling without replacement, meant that, from the total population of days in the Fall Semester, particular days for counting would be chosen at random and used only once. Confidence bounds and cost figures were estimated for each sample size, based on the 1972 statistics of the library. Time-and-motion study techniques were employed in the re-examination of functions currently performed by the exit-checkers at the library. Check-out and exit procedures were modified to increase efficiency, and rough estimates computed of the daily cost of counting exiting patrons under the old and new procedures. In a university setting, library patronage is subject to such variables as vacations and exam times; therefore a stratified random sampling technique, where each day of the week was selected a given number of times, might yield lower error estimates than those computed by the "pure" random sampling method used in this study. (SL)