You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information. |
Table of Contents Math Background Introduction to Probability Counting Rules | |
See also: events and probability |
When selecting elements of a set, the number of possible outcomes depends on the conditions under which the selection has taken place. There are at least 4 rules to count the number of possible outcomes:
n_{1}n_{2}* ...n_{j}.
Given a single set of n distinctively different elements, you wish to select k elements from the n and arrange them within k positions. The number of different permutations of the n elements taken k at a time is denoted P_{k}^{n} and is equal to
.
,
The numerator gives the permutations of the n elements. The terms in
the denominator remove the duplicates due to the same assignments in the
k sets (multinomial coefficients).
The combination rule is a special application of the partition rule, with j=2 and n_{1}=k. From n=n_{1}+n_{2} it follows that n_{2} can be replaced by (n-n_{1}). Usually the two groups refer to the two different groups of selected and non-selected samples. The order in which the n1 elements are drawn is not important, therefore there are fewer combinations than permutations (binomial theorem).
Last Update: 2006-Jän-17