The standard approach to the distribution of the number of runs appearing in a sequence is to make the result conditional on the number of each class of object which occurs. Illustrations are presented from the fields of psychology and zoology where invalid conclusions will be drawn under this assumption. By allowing the composition to fall at random, a multiple runs distribution is obtained which is conditional only on the total number of objects appearing in the sequence. Moments of the distribution are indicated along with an analysis of the normal approximation. Exact critical values for the number of runs in the case of two classes of objects are given so that a nonparametric test may be performed corresponding to the traditional runs test for randomness in an observed sequence.