1. CHAPTER 4 4-4:Counting Rules Instructor: Alaa saud Note: This PowerPoint is only a summary and your main source should be the book.

2. Counting RulesCounting Rules 1-Fundamental Counting Rule 2- Permutation 3- Combination Note: This PowerPoint is only a summary and your main source should be the book.

3.  In a sequence of n events in which the first one has k 1 possibilities and the second event has k 2 and the third has k 3, and so forth, the total number of possibilities of the sequence will be k 1 · k 2 · k 3 · · · k n 1-Fundamental Counting Rule Event 1Event 2Event n …………… k1k1 k2k2 knkn Note: This PowerPoint is only a summary and your main source should be the book.

4. 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, semi gloss, high gloss Use: outdoor, indoor How many different kinds of paint can be made if you can select one color, one type, one texture, and one use? Example 4-39: Note: This PowerPoint is only a summary and your main source should be the book.

5. Solution : ColorTypeTextureUse 7. 2. 3. 2 =84 Note: This PowerPoint is only a summary and your main source should be the book.

6. Q: A store manager wishes to display 8 different brands of shampoo in a row. How many different ways can this be done? Q:How many ways 5-digit passwords can be done ? Note: This PowerPoint is only a summary and your main source should be the book.

7.   Factorial is the product of all the positive numbers from 1 to a number. Note: This PowerPoint is only a summary and your main source should be the book.

8.   Permutation is an arrangement of objects in a specific order. Order matters. 2-Permutation Note: This PowerPoint is only a summary and your main source should be the book.

9. Suppose a business owner has a choice of 5 locations in which to establish her business. She decides to rank each location according to certain criteria, such as price of the store and parking facilities. How many different ways can she rank the 5 locations? Example 4-42: Note: This PowerPoint is only a summary and your main source should be the book.

10. Solution : 5!= 5.4.3.2.1= 120 Note: This PowerPoint is only a summary and your main source should be the book.

11. Example 4-44: A television news director wishes to use 3 news stories on an evening show One story will be the lead story, one will be the second story, and the last will be a closing story. If the director has a total of 8 stories to choose from, how many possible ways can the program be set up?. Since there is a lead, second, and closing story, we know that order matters. We will use permutations. Solution : Note: This PowerPoint is only a summary and your main source should be the book.

12.   Combination is a grouping of objects. Order does not matter. 3-Combination 3-Combination Note: This PowerPoint is only a summary and your main source should be the book.

13. Example 4-47: How many combinations of 4 objects are there. Taken 2 at a time? This is a combination problem, the answer is Solution : 4c24c2 Note: This PowerPoint is only a summary and your main source should be the book.

14. In a club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different possibilities are there? Example 4-49: Solution : There are not separate roles listed for each committee member, so order does not matter. We will use combinations. There are 35·10=350 different possibilities. Note: This PowerPoint is only a summary and your main source should be the book.

15. Permutation combination Means arrangement of things. Means selection of things Notes : 1. n P n=n! 2. n C n=1 3.The relation between combination and permutation Note: This PowerPoint is only a summary and your main source should be the book.

16. Probability and Counting Rules Note: This PowerPoint is only a summary and your main source should be the book.

17. Example 4-51: A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities : a- Exactly 2 are defective. Note: This PowerPoint is only a summary and your main source should be the book.

18. b-Non is defective. C- All are defective. D- At least 1 is defective Note: This PowerPoint is only a summary and your main source should be the book.

19. Example 4-52: A store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased. Solution: P( 1 TV Graphic and 1 Newstime) Note: This PowerPoint is only a summary and your main source should be the book.

20. Example 4-53: A combination lock consist of the 26 letters of the alphabet. If a 3- letter combination is needed, find the probability that the combination will consist of the letters ABC in that order.The same letter can be used more than once. Solution : Note: This PowerPoint is only a summary and your main source should be the book.

21. Example 4-54: There are 8 married couples in a tennis club. If 1 man and 1 woman are selected at random to plan the summer tournament, find the probability that they are married to each other. Solution : P(they are married to each other )= Note: This PowerPoint is only a summary and your main source should be the book.

22.  How many different ways can be selecting 4 bananas and 3 apples from 6 bananas and 8 apples? A)120 B)696 C)840 D)71 How many different words can we make using the letters A, B, E and L and repetition is not allowed? A-25 B-26 C-23 D-24 Anc. C Anc. D Note: This PowerPoint is only a summary and your main source should be the book.

23.  A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white? A)0.5 B)0.4 C)0.3 D)0.8  Given ten employees, three of them are males. If two employees are selected at random, what is the probability that both of them are females? A)1/15 B)3/50 C)7/15 D)21/50 Anc.C Anc.A Note: This PowerPoint is only a summary and your main source should be the book.

24.  If P(A)=0.6, P(B)=0.3and P(A or B)=0.7, given that A,B are not mutually exclusive, Find P(A and B)? A)0.2 B)1 C)1.5 D)0.18  The events A and B are such that P(A)=0.35, P(B)=0.55. Find P(A ∪ B) if A and B are independent events. a)0.19 b)0.71 c)0.9 d)1.02 ANC.A ANC.C Note: This PowerPoint is only a summary and your main source should be the book.

25.  A fair coin is toss and a dice is drown.Find the probability of getting a head and a number less than 5. a)1/3 b)2/12  4/3  6/9  The number of different ways to arrange four numbers from 2,4,6,8,7,9 : a)360 b)120 c)321 d)432 ANC.A Note: This PowerPoint is only a summary and your main source should be the book.