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Exploring Combinations and Permutations: Mathematical Concepts

Dive into permutations and combinations with practical examples like choosing TV ads, musical plays, book reviews, and more. Learn the formulas and see how they apply in various scenarios.

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Exploring Combinations and Permutations: Mathematical Concepts

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  1. Chapter 4.4 Combinations and Permutations

  2. Permutations • Permutations are used when arranging r out of n items in a specific order. nPr=

  3. Television ads • The advertising director for a television show has 7 ads to use on the program. If she selects one of them for the opening of the show, one for the middle of the show, and one for the ending of the show, how many possible ways can this be accomplished?

  4. School musical plays • A school musical director can select two musical plays to present next year. One will be presented in the fall, and one will be presented in the spring. If she has nine to pick from, how many different possibilities are there?

  5. Combinations • Combinations are used when the order or arrangement is not important • The formula for the number of combinations of r objects selected from n objects nCr=

  6. Combinations vs. permutations • Given the letters A, B, C, and D, list the permutations and combinations for selecting two letters.

  7. combinations • How many combinations of 4 objects are there taken 2 at a time?

  8. Book reviews • A newspaper editor has received eight books to review. He decides that he can use three reviews in his newspaper. How many different ways can these three reviews be selected?

  9. Committee selection • In a club there are seven women and five men. A committee of three women and two men is to be chosen. How many different possibilities are there?

  10. Promotional Program • The general manager of a fast-food restaurant chain must select six restaurants from eleven for a promotional program. How many different possible ways can this selection be done?

  11. Questions for a test • How many different tests can be made from a test bank of twenty questions if the test consists of five questions?

  12. Charity event • There are sixteen seniors and fifteen juniors in a particular social organization. In how many ways can four seniors and two juniors be chosen to participate in a charity event?

  13. Applying the concepts • Pg. 240 #1-7

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