ABSTRACT
Passing a line of ten persons waiting to buy a ticket at a movie theater on a Saturday afternoon, suppose we observe the arrangement of five males and five females in the line to be M, F, M, F, M, F, M, F, M, F. Would this be considered a random arrangement by gender? Intuitively, the answer is no, since the alternation of the two types of symbols suggests intentional mixing by pairs. This arrangement is an extreme case, as is the configuration M, M, M, M, M, F, F, F, F, F, with intentional clustering. In the less extreme situations, the randomness of an arrangement can be tested statistically using the theory of runs.
