Math119Sols2S11

Math119Sols2S11 - QUIZ 2 (SECTION 4-6, CHAPTER 5) SOLUTIONS...

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QUIZ 2 (SECTION 4-6, CHAPTER 5) SOLUTIONS MATH 119 – SPRING 2011 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% Show all work, simplify as appropriate, and use “good form and procedure” (as in class). Box in your final answers! No notes or books allowed. A scientific calculator is allowed. 1) (3 points). Which of the following is equal to 500 C 300 ? Box in one: a. 500! 300! b. 500! 200! c. 500! 300!200! FROM THIS POINT ON, DO NOT LEAVE P , C , OR FACTORIALS IN YOUR FINAL ANSWER. SIMPLIFY COMPLETELY! YOUR ANSWERS TO 2) THROUGH 5) WILL BE INTEGERS (“SIMPLE NUMBERS”). SHOW SOME WORK JUSTIFYING YOUR ANSWERS; DON’T JUST WRITE ANSWERS. Note : None of these answers is “one” or “none.” Some people get confused by what these kinds of problems are asking! 2) (5 points). Mr. Burns has nine employees. He requires four tasks to be done, each by a different employee. He will tell one of his employees to get him some coffee. Another will get him some Krispy Kreme donuts. Another will walk his dog. Another will mail a bribe to the local congressman. In how many ways can the four tasks be assigned among the nine employees? Method 1 There are 9 choices for the employee who gets the coffee. Assume one is chosen. Then, there are 8 choices for the employee who gets the donuts. Assume one is chosen. Then, there are 7 choices for the employee who walks the dog. Assume one is chosen. Then, there are 6 choices for the employee who mails the bribe. There are 9 ± 8 ± 7 ± 6 = 3024 ways .
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Method 2 Because we care about the “order” among the selected employees (it matters which employee gets which task), we are interested in the number of partial permutations, 9 P 4 = 9! 9 ± 4 () ! = 5! = 9 ² 8 ² 7 ² 6 ² = 9 ² 8 ² 7 ² 6 = 3024 ways. 3) (5 points). Remember, Mr. Burns has nine employees. He will select three of them to be the company’s official bowling team. How many possible bowling teams are there for Mr. Burns to choose from?
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This note was uploaded on 09/08/2011 for the course MATH 119 taught by Professor Staff during the Spring '11 term at Mesa CC.

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Math119Sols2S11 - QUIZ 2 (SECTION 4-6, CHAPTER 5) SOLUTIONS...

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