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Counting Problems and Combinations

Learn how to solve counting problems by combining simpler problems, using the principles of multiplication and addition. Practice with multiple examples.

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Counting Problems and Combinations

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  1. In Part 1 Module 6, we see counting problems is which two or more simpler problems, like those from Part 1 Modules 4 and 5, are combined into a single, more complicated problem. The following guidelines are usually important: Suppose A and B are tasks, where n(A) is the number of ways to perform Task A, and n(B) is the number of ways to perform Task B. Then: 1. The number of ways to perform both A and B = n(A) × n(B); 2. The number of ways to perform either A or B = n(A) + n(B). Part 1 Module 6 More counting problems

  2. In general, in counting problems and in probability, “And” means “multiply” “Or” means “add” n(A and B) = n(A) × n(B); N(A or B) = n(A) + n(B) when A, B are mutually exclusive. And, Or

  3. EXERCISE #1 Tonight there are 6 dishwashers and 5 servers working at the trendy new restaurant I Definitely Believe It's Tofu. Because it is a slow night the manager will select 2 dishwashers and 4 servers and send them home early.How many outcomes are possible?A. 75 B. 20 C. 3600 D. None of these. EXERCISE #2 Tonight there are 6 dishwashers and 5 servers working at the trendy new restaurant I Definitely Believe It's Tofu. Because it is a slow night the manager will select either 2 dishwashers or 4 servers and send them home early.How many outcomes are possible?A. 75 B. 20 C. 3600 D. None of these. Part 1 Module 6 More counting problems

  4. From The FUNDAMENTALIZER, Part 2 www.math.fsu.edu/~wooland/count/count17.html 1. Mr. Moneybags, while out for a stroll, encounters a group of ten children. He has in his pocket four shiny new dimes and three shiny new nickels that he will give to selected children. In how many ways may these coins be distributed among the children, assuming that no child will get more than one coin? A. 25,200 B. 3,628,800 C. 4,200 D. 604,800 2. Suddenly, he feels too cheap to give away all his coins. Instead, he will choose either four kids to receive the dimes or three kids to receive the nickels. In how many ways may the coins be distributed among the children, assuming that no child will get more than one coin? Exercises

  5. There are nine servers and six bussers employed at the trendy new restaurant The House of Hummus. From among each of these groups The International Brother/Sisterhood of Table Service Workers will select a shop steward and a secretary. How many outcomes are possible? A. 51 B. 540 C. 2160 D. 102 E. None of these Exercise

  6. There are nine servers and six busserss employed at the trendy new restaurant The House of Hummus. The International Brother/Sisterhood of Table Service Workers will either select a shop steward and a secretary from among the servers, or they will select a shop steward and a secretary from among the bussers. How many outcomes are possible? A. 51 B. 540 C. 2160 D. 102 E. None of these Exercise

  7. A couple is expecting the birth of a baby. If the child is a girl, they will choose her first name and middle name from this list of their favorite girl’s names: Betty, Beverly, Bernice, Bonita, Barbie. If the child is a boy, they will choose his first name and middle name from this list of their favorite boy’s names: Biff, Buzz, Barney, Bart, Buddy, Bert. In either case, the child's first name will be different from the middle name. How many two-part names are possible? A. 50 B. 600 C. 61 D. 900 EXERCISE

  8. The mathematics department is going to hire a new instructor. They want to hire somebody who possesses at least four of the following traits: 1. Honest; 2. Trustworthy; 3. Loyal; 4. Gets along well with others; 5. Good at math; 6. Good handwriting In how many ways is it possible to combine at least four of these traits? A. 360 B. 15 C. 22 D. 48 E. None of these Exercise #5

  9. The engineers at the Gomermatic Corporation have designed a new model of automatic cat scrubbing machine, and a new model of robotic dog poop scooper. Now it is the Marketing Department's job to come up with catchy, high-tech sounding names for the products. For each product they will randomly generate a three-syllable name, such as Optexa, by choosing one syllable from each of the following categories: First syllable: Apt; Opt; Axt; Emt; Art; Ext. Second syllable: a; y; e. Third syllable: va; xa; ta; ra. How many outcomes are possible, assuming that the two products will not have the same name? A. 5112 B. 143 C. 2556 D. none of these Exercise #7

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