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# Applied Math 40S March 4, 2008

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More applications of permutations of non-distinguishable objects and introduction to combinations.

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### Applied Math 40S March 4, 2008

1. 1. The difference between Combinations and Permutations The Mastermind by jnthnhys Combination (224365) by Cellach
2. 2. Probability and Statistics
3. 3. HOMEWORK If 8 books are arranged on a shelf, what is the probability that 3 particular books are together?
4. 4. HOMEWORK (a) In how many ways can the letters of the word GEOMETRY be arranged so that vowels and consonants alternate? (b) In how many of these ways is Y the last letter? (c) If one of these quot;wordsquot; is randomly selected, what is the probability that Y is the last letter?
5. 5. HOMEWORK Suppose that, when you go home from school, you like to take as great a variety of routes as possible, and that you are equally likely to take any possible route. You will walk only east or south. How many ways can you go from the school to home? What is the probability that you will walk past the post office on your way home?
6. 6. HOMEWORK Suppose that, when you go home from school, you like to take as great a variety of routes as possible, and that you are equally likely to take any possible route. You will walk only east or south. How many ways can you go from the school to home? What is the probability that you will walk past the post office on your way home?
7. 7. Design an experiment using coins to simulate a 10 question true/false test. What is the experimental probability of scoring exactly 70% on the test if you guess each answer? Let's think about this using what we've just learned ... Solve for the exact theoretical probability of getting quot;at least 7quot; out of ten on this test.
8. 8. Combinations (the quot;Choosequot; Formula) A combination is arrangement of objects On the calculator ... where order does not matter. Press: [MATH] n is the number of objects [<] (Prb) available to be arranged [3] (nCr) r is the number of objects that are being arranged. Examples: How many different 5 person There are 15 people on the student council. teams can be made from 10 How many 3 person subcommittees can be people? made on the council?
9. 9. There are 10 football teams in a certain conference. How many games must be played if each team is to play every other team just once?
10. 10. HOMEWORK Design an experiment using coins to simulate a 10 question true/false test. What is the experimental probability of scoring at least 70% on the test if you guess each answer? Let's think about this again using what we've just learned ... Solve for the exact theoretical probability of getting quot;at least 7quot; out of ten on this test.
11. 11. HOMEWORK (a) How many numbers of 5 different digits each can be formed from the digits 0, 1, 2, 3, 4, 5, 6? (b) If one of these numbers is randomly selected, what is the probability it is even? (c) What is the probability it is divisible by 5?
12. 12. HOMEWORK Seven people reach a fork in a road. In how many ways can they continue their walk so that 4 go one way and 3 the other?