8. A teacher has 10 different mathematics books. Of these books, 5 are on Algebra, 3 are on Calculus and 2 are on Trigonometry. The teacher arranges all 10 books in random order on a shelf.
a) Find the probability that the Calculus books are next to each other and the Trigonometry books are next to each other. \section*{In this question you must show detailed reasoning.} b) Find the probability that 2 of the Calculus books are next to each other but the third Calculus book is separated from the other 2 by at least 1 other book.