Details of the North American Numbering Plan (NANP), the numbering plan for the Public Switched Telephone Network in North America and the Caribbean, can be found at

By the way, this plan was invented at AT&T Bell Laboratories in 1947, was later administer by Bellcore with the 1984 split of AT&T, and is now administered by Lockheed Martin. The NANP is part of the larger International Telecommunications Union E.164 specifications for telephone number worldwide. You can see a list of all the E.164 country codes at

A variety of applications of the pigeonhole principle can be found on the Interactive Mathematics and Miscellany site.

A biography and a portrait of Dirichlet can be found at the History of Mathematics Archive at the University of St Andrews, Scotland.

A biography and a photo of Frank Plumpton Ramsey can be found at the History of Mathematics Archive at the University of St Andrews, Scotland.

An excellent introduction to combinations and permutations can be found at the Amazing Mathematical Object Factory, part of Canada’s SchoolNet project.

See the link provided for page 250

A Java applet, written by Jeremy Baer in the Computer Science Department at the University of Washington to look at patterns of binomial coefficients in Pascal’s triangle that have a particular set of divisors, can be found at

An interesting discussion of the binomial theorem, including historical information, derivations, and visualizations, by Guillermo Francia, III and Peter Flusser can be found at

A brief biography of Vandermonde can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.

Page 261

A biography and a portrait of Pierre Laplace can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.

Expository materials and interactive Java applets on probability and statistics can be found at the Virtual Laboratories in Probability and Statistics site, written by Kyle Siegrist and Jason York at the University of Alabama at Huntsville.

The probabilities of winning different prizes at the UK National Lottery can be found at

A lottery simulation written in Java Script that can be used to choose six numbers from the numbers 1,2,…,49 and then see how many numbers you selected of the six numbers selected at random by the program. (Of course, the probability of winning is extremely slim and there is no prize to win!). This page also discusses the odds of winning.

Coyote’s site provides the opportunity to learn more about the Monty Hall Three Door Puzzle and to experiment with a nicely designed interactive simulation of the puzzle. This site also considers the generalization of the puzzle to more than three doors and provides C source code for a simulation where the number of doors is an input value.

Another site describing the Monty Hall problem and offering a solution, together with an interactive applet, is the Grey Labyrinth Puzzle Site

Material about Bernoulli trials and interactive Java applets for simulating coin flips and other experiments can be found at the Bernoulli Trials section of the Virtual Laboratories in Probability and Statistics site.

A biography and a portrait of James Bernoulli (also known as Jacob I and Jacques) can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.

Material about the probabilities of outcomes for different experiments with dice and interactive Java applets can be found at the Dice Trials section of the Virtual Laboratories in Probability and Statistics.

More information about expected values, properties of expected values, variances, and other related topics can be found in the Expected Values section of the Virtual Laboratories in Probability and Statistics site.

A biography and a photo of Chebyshev can be found at the History of Mathematics Archive at the University of St Andrews, Scotland.

The Birthday Problem page, constructed by George Reese, is concerned with the problem that at least two people in a room have the same birthday. This site provides a Java applet that can be used to run simulations, as well as a solution to this problem.

You can find information about counting with repetition at

The Combinatorial Object Server, developed by Frank Ruskey, provides interactive programs for generating all the permutations, all the k-permutations, all the combinations, and all the combinations with at most k elements of a set with n elements, where n and k cannot exceed some reasonable large values. It also has programs for generating all the permutations and combinations of a multiset, which can be used to generate permutations and combinations when repetition of objects is allowed. Source code in C and/or Pascal can be downloaded for many of these programs.

See the link to the Combinatorial Object Server (page 296 )

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