Figure 10.1.1: Example: Counting the number of cupcake selections. A bakery sells 6 different varieties of cupcakes (chocolate. vanilla, red velvet, etc). How many ways are there to fill a box with 24 cupcakes from the 6 varieties? The order in which the cupcakes are selected is unimportant; all that matters is the number of each variety in the box after they are chosen. 1'.-"-#I\"'.'--r ALE}! * iiii i' The answer to the cupcake counting problem is 118755 too many to count by hand. While counting cupcake selections may not seem like a compelling application, the same techniques can be used to count the number of ways 24 identical tasks can be assigned to a network of 6 processors which in turn can be used to calculate the probability that a random assignment distributes the workload evenly among the 6 processors