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Name: Cory M.
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Question:
Where can I find information to calculate how many variations there are to a finite set of numbers?



Replies:
I assume that you are referring to the number of permutations and/or combinations that are possible if "m" objects are selected randomly from "n" such objects. You can search the web for the topic "calculation permutations combinations" and obtain many "hits". The difficulty is that the subject is treated poorly both on most of those sites, and even in most standard statistics texts. For example the web site "mathforum", which usually treats many math topics well, addresses permutations and combinations by giving a few examples and then adopts the attitude, "Now you see how it goes." They even close with the caveat: "One of the hardest parts about doing problems that use permutations and combinations is deciding which formula to use." That is NOT a good sign that the topics are explained very well.
See: http://mathforum.org/dr.math/faq/faq.comb.perm.html

The best web site I could find on the topic is: www.mis.coventry.ac.uk/jtm/ This site is a real find. It is an on-line math text "JUST THE MATHS" by A.J. Hobson. It starts from the very basics and proceeds through calculus, differential equation... For permutations and combinations see Chapter 19. An excellent resource for all students taking anything from introductory algebra to advanced applied math.

Vince Calder


Cory,

I cannot answer this question exactly because you do not identify what kinds of variations: order, value, .... You also do not identify what sort of numbers: real, integer, all different, some the same, .... I can direct you to the correct words to look for. In math texts and library books about math, two very important words are "combination" and "permutation". These are the two most common ways to vary a finite set of numbers. Both refer to taking a smaller set of numbers from a larger set of numbers. An example would be having a bag of numbers from 1 to 15. Choosing a set of three numbers from the bag is combination. Choosing a set of three numbers one at a time, keeping track of the order, is a permutation. "Probability" and "sets" are more general words that apply.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College



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