Math 1620 Week 1, Class 2
Math 1620 Week 1, Class 2 MATH 1620
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This 5 page Class Notes was uploaded by Mariah Figueiredo on Wednesday January 27, 2016. The Class Notes belongs to MATH 1620 at Rensselaer Polytechnic Institute taught by Wing Sze E Kam in Spring 2016. Since its upload, it has received 28 views. For similar materials see Contemporary Mathematical Ideas in Society in Mathematics (M) at Rensselaer Polytechnic Institute.
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Date Created: 01/27/16
Week1 11.3-11.4 Combinations, Fundamentals of Probability Spring 2016 Permutation vs Combination Permutation Combination Order MATTERS!! DOES NOT MATTER Formula n ! nP r n ! nPr▯ nCr▯ ▯ ▯n▯r ! r ! r ! n▯r ! Permutation or Combination? 1. How many different 4-letter passwords can be formed from the letters A, B, C, D, E, F, and G if no repetition of letters is allowed? 2. 50 people purchase raffle tickets. 3 winning tickets are selected at random. In how many different ways can the prizes be awarded? Example 1 A 4-person committee is to be chosen from a group of 7 students. How many different committees could be formed? Q: How did we get the formula for combination? A: Let’s illustrate this with an example – Example 2 Suppose we have 4 letters A, B, C, and D. The number of permutations of these 4 letters taken 3 at a time is 1 The permutations are: There are combinations. Number of permutations = Number of combinations Example 3 There are 13 children on a playground, 8 boys and 5 girls. a. Determine the number of ways to select 7 from them. b. Find the number of ways to select 7, if 4 are boys and 3 are girls. 2 Fundamentals of Probability Q: What is an “experiment”? A: An experiment is a process that is e.g. rolling a die, drawing a card from a deck, etc. Probability of an event, number of outcomes in E P E ▯ ; tota number of possible outcomes 0 ▯ P E ▯1 ; P E ▯ P not E ▯1 Example 4 A die is tossed once. Find the probability of rolling a. a 5 b. a number NOT a 5 c. a number < 8 d. a number > 8 3 Example 5 A jar has 6 black balls, 4 red balls, 7 blue balls. If a ball is drawn at random, find the probability that it is a red one? Example 6 Suppose 1 card is dealt from a standard 52-card deck. Find the probability of being dealt a. a Queen b. a diamond c. a picture card d. NOT a picture card 4 Suggested HW 11.3 : # 10, 13, 18, 28, 31, 37, 40 11.4 : # 5, 6, 12, 13, 16, 18 Exercises 11.3 WRITE the formula for nC r and use it to evaluate #10, #13, #18, and #28. #10. 12C 5 #13. C7 7 #18. C 6 0 5C 1 7 2 #28. 12C 3 #31. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take? #37. In how many ways can a committee of 4 men and 5 women be formed from a group of 7 men and 7 women? #40. A mathematics exam consists of 10 multiple-choice questions and 5 open-ended problems. If an examinee must answer 8 of the multiple-choice questions and 3 of the open-ended problems, in how many ways can the questions and problems be chosen? Exercises 11.4 For #5 and #6, a die is rolled Find the probability of rolling #5 a number < 3. #6 a number > 4. For #12, #13, #16, #18, a card is dealt from a standard 52-card deck. Find the probability of being dealt #12 a jack. #13. a club. #16. a card > 3 and < 7. #18. the ace of clubs. 5
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