Analysis: The solution above appears to be a straightforward application of the Multiplication Principle: to count the total number of ways of doing a task, one can multiply the number of ways of performing the subtasks that comprise the whole task (hence the answer 28*9). However, this answer is nearly two times too large. The main reason for this is that the solution presented above imposes an ordering on the blue stripes (students are unaware of this), when the order in which the stripes are painted is immaterial: the question is only interested in counting finished flags. In particular, the solution above first chooses six blue stripes, and then (possibly) chooses additional blue stripes. Therefore, the solution has ordered the blue stripes into two “groups”: the first six blue stripes and any additional blue stripes after that.