Just one question now...The rest I get just fine! If there are 10 identical yellow balls and 15 identical purple balls then how many distinguishable arrangements are possible if two yellows CANNOT be next to each other? ANSWER: 8008 My issue is not figuring out the answer, but the calculator equation that leads to it. This thing has been extremely annoying, but I'm "very" close to figuring out the equation (I have a TI-83+). Thanks!