Basic Counting PrinciplesSum Rule Principle: Assume some event E can occur in m ways and a second event F can occur in n ways, and suppose both events cannot occur simultaneously. Then E or F can occur in m + n ways. In general, if there are n events and no two events occurs in same time then the event can occur in n_{1}+n_{2}..........n ways. Example: If 8 male processor and 5 female processor teaching DMS then the student can choose professor in 8+5=13 ways. Product Rule Principle: Suppose there is an event E which can occur in m ways and, independent of this event, there is a second event F which can occur in n ways. Then combinations of E and F can occur in mn ways. In general, if there are n events occurring independently then all events can occur in the order indicated as n_{1} x n_{2} x n_{3}.........n ways. Example: In class, there are 4 boys and 10 girls if a boy and a girl have to be chosen for the class monitor, the students can choose class monitor in 4 x 10 = 40 ways. Mathematical Functions:Factorial Function: The product of the first n natural number is called factorial n. It is denoted by n!, read "n Factorial." The Factorial n can also be written as Example1: Find the value of 5! Solution: 5! = 5 x (51) (52) (53) (54) = 5 x 4 x 3 x 2 x 1 = 120 Example2: Find the value of Solution: == 10 x 9=90 Binomial Coefficients: Binomial Coefficient is represented by n_{Cr} where r and n are positive integer with r ≤ n is defined as follows: Example: 8_{C2} === 28.
Next TopicPermutations & Combinations
