Variations in a Finite Set
Name: Cory M.
Where can I find information to calculate how many variations there are to a finite
set of numbers?
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.
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.
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
Illinois Central College
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Update: June 2012