For question 20, think "There are 8 horses that could place first, then if one places first, there are 7 horses that could place second, and then if that happens, there are 6 left that could place third". So for that one, the answer should be 8*7*6. This is an example of when Order matters. Like if Horse A gets in 1st place and horse B gets in second place, then that is a different scenario from if Horse B gets in first place and horse B gets in second, thus using nPr is appropriate and not nCr. You want to use nPr when order matters.
I absolutely hate the way question 27 is worded. To me, there is only one combination of 3 Blue balloons you should be able to make, however the question implies that every blue balloon is different, and so the question is better worded like: Lynn has 12 Distinct Balloons, how many 3 balloon bouquets can she make? With this wording, it makes it more clear that you should use nCr because order DOES NOT matter, and a bouquet with balloons ABC is the same as a bouquet with balloons BCA. In this case use nCr or 11C3 = 220
Question 64: I know this as a binomial distribution... I'm not sure if you learned it as this. So I'm not sure of an easy way to teach it.. =P Maybe you would not mind looking this up and seeing how it would fit with 3C2*(.70)^2*(.30)^1 =]
Personally the wording of such questions like 27 made me stop doing those types of questions in the Destroyer.. they are a bit misleading.
