WT 3rd Pg 102 #14

[doclkk]

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

3/5



I don't understand how the book gets 48 for the possibilities that the girls will be seated next to each other besides writing them out.

[Ben Ku]

If Oprah and Penny are sitting next to each other, they can essentially be treated as one person. So basically we want all combinations of L, M, N, and O/P, which is 4! = 24. However, there are two ways they can sit together: Oprah then Penny, and Penny, then Oprah. So the total combinations where Oprah and Penny are seated next to each other is 2 x 24 = 48.