1. The problem statement, all variables and given/known data 4 books by Shakespeare, 2 books are Dickens and 3 by Conrad are chosen for the problem. The question is to find the number of ways in which the books can be arranged s.t. the 3 Conrad books are separated. 2. Relevant equations 3. The attempt at a solution n(C separated) = n(w/o any restrictions) - n(3 C's together) - n(2 C's together). n(w/o any restrictions) = 9! because there are 9 items to be put in 9 places. n(3 C's together) = 3! * 7! because the 3 C's form a cluster: 3! for items within the cluster and 7! for all the items, considering the cluster as an item. n(2 C's together) = ... This is the tricky one as only 2 C's form a cluster and the number of places available for the other C depends on whether the cluster is at either of the edges of not. The answer is supposed to be 151,200 (from the back of the textbook), but I can't happen to get it.