Unit 4 Section 4-5

4-5: Counting Rules  To determine the number of possible outcomes for a sequence of events we use one of three counting rules:  Fundamental Counting Rule  Permutation Rule  Combination Rule  Fundamental Counting Rule: In a sequence of n events in which the first one has k 1 possibilities, the second one has k 2 possibilities, and so forth…the total number of possibilities will be k 1 * k 2 * k 3 *…k n (Multiply the possibilities)

 Example 1: A coin is tossed and a die is rolled. Draw a tree diagram to represent the total number of outcomes. Verify your findings using the fundamental counting rule.  Example 2: A paint manufacturer wishes to manufacture several different paints. The categories include: Color : red, blue, white, black, green, brown, yellow Type : latex, oil Texture : Flat, semigloss, high gloss Use : Indoor, outdoor How many different kinds of paint can be made if a person can select one color, one type, one texture, and one use? Section 4-5

 Example 3: The digits 0, 1, 2, 3, and 4 are to be used in a four-digit ID card. How many different cards are possible if repetitions are permitted? Section 4-5

 Factorial Notation – uses an ! as its notation.  5! Means 5 * 4 * 3 * 2 * 1  Special Definition : 0! = 1  Example 4 : Simplify  2!  4!  (5 – 2)!  5! – 2  3! + 5! Section 4-5

Homework:  Pg 220 – 221 : 1 – 12, 13 c, d, h, i Section 4-5