[manayay]

You have n books on algebra, k on probability and l on calculus. The
books are all different. If you place them on a shelf at random what is the
probability that
(a) Books on the same subject are adjacent.
(b) Books on the same subject are in alphabetical order by author, but not
necessarily adjacent.
(c) Books on the same subject are adjacent and within each subject they are
in alphabetical order.