6 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 chooses 5 of the books at random.
- Find the probability that 3 of the books are on Algebra.
The teacher now arranges all 10 books in random order on a shelf.
- 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.}
- 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.