\(\textbf{1.1 - COUNTING PRINCIPLES}\)
\(\textbf{COMBINATORICS is a branch of mathematics dealing with ideas and }\)
\(\textbf{methods for counting and arranging. Combinatorics applies mathematical }\)
\(\textbf{operations to count quantities that are much too large to be counted the}\)
\(\textbf{conventional way.}\)
\(\textbf{Counting Techniques}\)
\(\textbf{A. Tree Diagrams}\)
\(\textbf{B. Factorial (n!)}\)
\(\textbf{FUNDAM ENTAL OR MU LTI PLICATIVE COU NTING PRI NCIPLE}\)
\(\textbf{lf a task or process is made up of stages with separate choices, the total number}\) \(\textbf{of choices is:}\) \(\textbf{m x n x p x....., where m isthe numberof choicesforthefirst stage,}\) \(\textbf{n is the number of choices for the second stage,}\) \(\textbf{p is the number of choices for the third stage, and so on.}\)
\(\textbf{ADDITIVE COUNTING PRINCIPLE OR RULE OF SUM}\)
\(\textbf{lf one mutually exclusive action can occur in m ways, a second in n ways, a third }\) \(\textbf{in p ways, and soon, then there are m + n + p +. . . . . ways in which one of these actions }\) \(\textbf{can occur.}\)\(\textbf{L.2 - FACTORIAL NOTATION}\)
\(\textbf{Factorial - the product of all positive integers less than or equal to n.}\) \(\textbf{n!=nx(n-1)x(n-2)x(n-3)x...x3x2x1}\)
\(\textbf{For example:}\)
\(\textbf{1!=1}\)
\(\textbf{ 2!=2 x 1}\)
\(\textbf{3!=3 x 2 x 1}\)
\(\textbf{ 4!=4 x 3 x 2 x 1}\)
\(\textbf{}\) \(\textbf{}\)