Permutations and combinations textbook recommendations

You are looking for references on combinatorics. There are many lecture notes around the 'net, hiding under names like "discrete mathematics" (elementary combinatorics of the sort you are looking for is one of the main dishes in such a course).

Perhaps the best reference for self study is Kenneth Bogart's "Combinatorics through Guided Discovery". Another good resource is Bogart, Drysdale, Stein "Discrete Math for Computer Science Students". Both are available in full as PDFs for free.

I highly recommend Schaum's Outline of Combinatorics by V. K. Balakrishnan.

It contains lots of small examples that are manageable by a beginner, and shows you how to do it in a straightforward manner.