Incorrect Solution to Problem 1: Consider the flag shown below. Each stripe must be labeled with a color: red, green, or blue. Since at least six blue stripes are required, one can begin by choosing six stripes to color blue. There are C(8,6) = 28 ways to do this. Once the six blue stripe minimum is fulfilled, the remaining two stripes (whichever ones they are) can each be colored in any one of three ways (red, green, or blue). Therefore, there are 3*3 = 9 ways to finish coloring the stripes, for a total of 28*9 = 252 ways to color the stripes of the flag.