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|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:
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 Pkn 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 n1=k. From n=n1+n2 it follows that n2 can be replaced by (n-n1). 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-Jšn-17