All four of these problems involve aspects that must be handled carefully. Many students do not see these delicate points, nor do they see any substantive differences in the way these four problems are best handled. This paper is intended to draw attention to some of the errors in thinking that students fall victim to in solving counting problems such as these, examine the differences between the correct solutions to these problems and the solutions often given by misdirected students, and provide some problems to encourage practice in this challenging area.