Word Translations (Page 195, #4)

[tomhpae]

If Laure, Mary, Nancy, Oprah, and Penny sit randomly in a row, what is the probability that Oprah and Penny are NOT next to each other?


The explanation on Page 198 lists out all the possibilities. I know I won't have time to do this on the real test. So what's the mathematical method to get "8 Arrangements in which Oprah and Penny ARE next to each other"? (I understand the whole 1-X concept so that's why I'm trying to subtract their possibility of sitting next to each other from 1).

[tim]

to get the 8 arrangements of those two, just consider which seats they can occupy: 12, 23, 34, or 45. Now each of these accounts for two arrangements because the people can sit in either order, so that gives you the 8. Of course, for each of these 8, there are 6 ways the remaining people can sit, for a total of 48 undesirable outcomes. Using a 1-x approach is great for this one, because now you just subtract 48 from the total of 120 ways all five can sit to get your answer..