Summary of our combinatorial rules
Here are our main rules for counting sets in connection with finite sample spaces with equally likely
outcomes.
Multiplicative Rule: Suppose each element of a set can be viewed as a choice, and we can organize this
choice into two stages. Suppose that the first stage choice can be made In m ways, and for each first
stage choice the second stage choice can be made in n ways. Then the overall choice can be made in mn
ways, and hence the set has mn elements.
This rule of course can be extended to the case where the overall choice can be organized into k stages.
Strings: suppose a set consists of n symbols. Then the number of strings of k symbols from these n
symbols (repetition ALLOWED) is
.
k
n
Permutations: Suppose a set consists of n symbols. Then a permutation of k elements from these n is a
string of k of the n symbols, repetition NOT ALLOWED. The number of permutations of k elements from
n is
(
)
(
)
(
)
!
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Luikonnen
 Sets, Counting, Probability, South African National Roads Agency, nCk, stage choice, binomial coefficient nCk

Click to edit the document details