If Julie includes one of the colors that cover three cupcakes, she must also include the other color that covers three cupcakes. This is because she must make ten cupcakes total, and all of the other colors cover an even number of cupcakes, so there is no way to make ten with three and some combination of even numbers. Thus, if she includes blue and violet, she has four cupcakes left to choose. There are three ways in which she can choose four cupcakes if she chooses colors that cover two (green and orange, green and yellow, or orange and yellow). Alternately, she can choose a color that covers four (red). Finally, if she doesn't include any colors that cover three cupcakes, she must choose all of the other cupcakes in order to make ten. So, 5 :)
