Question

1. A State issues car license plates with three letters followed by three numbers (for example, FGH831 or BBB222). How many different license plates are possible? (Note that letters or numbers may repeat in the license plate. Hint: Use the Fundamental Counting Rule for this question.) There are five students who are interested in presenting their final project to the class, but there is only time for three presentations. The five students are Amy, Bob, Chun, Dan and Ed. 2. List all the possible combinations of three students the professor could pick. The order of the presentations does not matter. To save space, you can just use the first initial of each name if you like. 3. How many different combinations are there? 4. Now, use the Counting Rule for Combinations formula to calculate the number of combinations and compare your results. 5. Which approach was easier? 6. If the professor picks three students at random by drawing three names from a bat what is the probability that the three students chosen are Amy, Chun and Dan? Now, assume that the first student chosen will present on Monday, the second will present on Wednesday and the third will present on Friday. In other words, now the order the students are chosen matters. Use this situation to answer questions 7.8 and 9. 7. If the professor chooses Amy, Chun and Dan to present, list all the possible permutations of how their presentations could be distributed over the three days. MacBook

Answer 1

1. Total Alphabets = 26

Total numbers = 10

Total number of different license plate = 26*26*26*10*10*10 = 17,576,000

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