Originally Posted by

**zmogggggg**
A) C is Cinderella and H is Hobbit. The subset CBBBH has 5 elements and there are 6 possible locations for them in the set of 10 books, and 8! ways to arrange the remaining 8 books for each of these 6 positions

CBBBHBBBBB

BCBBBHBBBB

BBCBBBHBBB

BBBCBBBHBB

BBBBCBBBHB

BBBBBCBBBH

so that there are 8!*6*2 = 483840 ways 3 books can separate C and H (C and H can be interchanged, hence factor of 2). Then

P(3 books in between C and H) = 483840 / 10! = .134

B) I think you included a factor of 6 twice on accident. Divide your answer by 6 and it should be good.