Basic principles are addressed at http://www.cs.odu.edu/~toida/nerzic/content/counting/basic_principles.html.

For a basic introduction see http://www.math.uah.edu/stat/comb/comb2.html and http://www.math.uah.edu/stat/comb/comb3.html.

In April 2002, Preda Milhailescu announced that he had proved Catalan's conjecture.

For a list of some of the items counted by the Catalan numbers and pictures of them, see http://www-history.mcs.st-and.ac.uk/~history/Miscellaneous/CatalanNumbers/catalan.html.

For information about generating permutations with links to implementations, see http://www.cs.sunysb.edu/~algorith/files/generating-permutations.shtml. The site http://www.theory.csc.uvic.ca/~cos/cos.html by Frank Ruskey provides programs for generating permutations and combinations with various restrictions and generalizations. My own source code for generating permutations is perm.c.

See the Virtual Laboratories in Probability and Statistics at http://www.math.uah.edu/stat/. The Probability Web at http://www.mathcs.carleton.edu/probweb/probweb.html is a collection of probability resources.

A simulation is at http://www.mste.uiuc.edu/reese/birthday/intro.html.

Check http://www.ping.be/~ping1339/tel.htm.

For a discussion of the binomial theorem, see http://www.inetarena.com/~pdx4d/ocn/binomial.html.

Patterns in Pascal’s triangle is the topic of the site http://www.cs.washington.edu/homes/jbaer/classes/blaise/blaise.html. A biography of Pascal is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html.

A discussion of the Pigeonhole Principle and lots of examples are at http://www.cut-the-knot.com/do_you_know/pigeon.html. A biography of Dirichlet is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dirichlet.html.