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NAME: MATH125: Unit 8 Submission Assignment Answer Form Counting Techniques ALL questions below must be answered. Show ALL step-by-step calculation . Upload this modified Answer Form to the intellipath Unit 8 Submission lesson. Make sure you submit your work in a modified MS Word document; handwritten work will not be accepted . If you need assistance, please contact your course instructor. Part A: Combinations and Permutations 1. Differentiate between permutations and combinations. How are they different? What is the formula for each? (15 points total for Question 1) How are they different? (5 points) Permutations rely on order and combinations do not. Permutation Formula (5 points) N!/(n-r)! Combination Formula (5 points) N!/r!(n-r)! 2. Each state has a standard format for license plates that includes a set number of alphanumeric characters. For this assignment, you can insert a picture of your state’s non-personalized license plate or provide a sample of the format in text. (20 points total for Question 2) Your State’s Name (1 point) North Carolina

Pictu re of a Licen se Plate from Your State (or a Samp le) (1 point ) Describe the Character Rule for Your State’s Non-personalized License Plates (1 point) 8 characters can be on the license plate. You can use any letters and number 0-9 and special characters. a. Determine the number of different license plates that can be created using the following format. Assume that a license plate consists of seven alphanumeric characters using numbers (0–9) and capital letters (A–Z). Find how many unique license plates can be printed using any of the 36 alphanumeric characters without duplication in each of the seven alphanumeric characters, i.e., no alphanumeric character appears more than once in any license plate. (This question is NOT related to your state’s license plates in the initial 3 parts above). I I Is this a permutation or combination? Why? (2 points) Combination because the order isn’t specified What formula from Question 1 will you use to solve the problem? (1 point) N!/r!(n-r)!

Number of unique license plates that can be printed : (2 points) (36)!/7!(36-7)! 8347680 Show your work here (2 points) : b. You and a friend are witnesses of a car accident in your state. But you can only remember a few of the first alphanumeric characters on the license plate. How many alphanumeric characters do you remember? (1 point) 2 (Select a number from 2 to 5) What are the characters at the beginning? (1 point) AD How many license plates start with these alphanumeric characters? (2 points) 630 Show your work here (2 points) : How many license plates have been eliminated? (2 points) 8347050 Show your work (2 points) :

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3. Your community has asked you to help the YMCA sports director organize a season of sports. You need to put together the teams. For the soccer teams, athletes signed up for one of three different age groups (Little Tykes, Big Kids, and Teens). (15 points total for Question 3) What formula from Question 1 will you use to solve the problem? (1 point) N!/(n-r)! Is this a permutation or combination? Why? (2 points) Permutation How many kids signed up for “Little Tykes”? (1 point) 40 (Select a multiple of 10, of at least 20) How many kids signed up for “Big Kids”? (1 point) 30 (Select a multiple of 10, of at least 20) How many kids signed up for Teens? (1 point) 20 (Select a multiple of 10, of at least 20) How many total students signed up for soccer? (1 point) 90 (enter total form the three groups above)

Use the formula and values, from question above, to answer the following: Show your work here: (2 points) Show your work here: (2 points) Part B: Probabilities and Odds 4. For this set of exercises, you will need a single standard six-sided die. If you do not have one, you can use a virtual die: https://www.random.org/dice/ ( 40 points total for Question 4) a. First, differentiate between odds and probability . How are odds and probability different? (2 points) The probability an event will occur is the fraction of times you expect to see that event in many trials. The odds are the probability that the event will occur How many different ways can you create teams of 10 for the “Little Tykes” grade level? (2 points) (40)!/(10)! 847,660,528 If age levels did not matter, how many different ways can you create teams of 10 from the total number of soccer players? (2 points) 5,720,645,481,903

divided by the probability that the event won’t occur What is the odds in favor ratio? (3 points) P(e)/p(not e) What is the probability of an event ratio? (3 points) Favorable outcomes/total outcomes b. Reflect on the previous question’s answer outcome. First, convert the fraction to a percent. Percent Probability Theoretical Probability (Rounded to the nearest whole percent.) (2 points) 16.6% What are the odds of rolling a three (use the proper ratio from above)? Simplify all fraction answers. (2 points) 1/6 What is the theoretical probability of rolling a three (use the proper ratio from above)? Simplify all fraction answers. (2 points) 1/6

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Next, use the likelihood scale table above to select the term that best describes your answer. Likelihood Scale Term (2 points) Unlikely c. What if someone challenged you to never roll a 3? If you were to roll your single six- sided die 18 times, what would be the theoretical probability of never getting a three? Also, list the likelihood scale term from the table above. Percent Probability Solution (Rounded to the Nearest Whole Percent) (2 points) 18 x 5/6 Likelihood Scale Term (2 points) 83% likely Show your work here: (2 points) d. After 18 rolls, what would be the theoretical probability of getting a three on at least one of those rolls? Also, list the likelihood scale term from the table above. Percent Probability Empirical Probability (Rounded to the Nearest Whole Percent) (2 points) 1/18 =.055= 5.5%

Likelihood Scale Term (2 points) Rare Show your work: (2 points) e. Roll the die 18 times and keep track of what is rolled in the table below. Remember, if you do not have one, you can use virtual dice: https://www.random.org/dice/ (2 points) Roll # Dice Roll # Dice Roll # Dice Roll 1 3 Roll 7 2 Roll 13 2 Roll 2 3 Roll 8 1 Roll 14 5 Roll 3 6 Roll 9 5 Roll 15 ?1 Roll 4 2 Roll 10 1 Roll 16 2 Roll 5 4 Roll 11 3 Roll 17 5 Roll 6 ?2 Roll 12 6 Roll 18 4 f. Based on your die rolls, what is the experimental probability of rolling a three, out of 18 rolls? Also, list the likelihood scale term from the table above. Percent Probability Experimental Probability (Rounded to the Nearest Whole Percent) (2 points) 3/18 Likelihood Scale Term (2 points) .1667 unlikely Show your work here: (2 points) What do you notice about the answers for parts c and d above? (2 points) Theoretical probability increases the chances

With regard to the likelihood scale terms for each, how did this differ from both the theoretical and empirical probabilities? (2 points) Rolling a 3 on a single dice theoretically was rare and the likelihood of rolling 3 on 18 turns was unlikely.

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