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Chapter 6: Counting

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Discrete Mathematics and its Applications
Pages: 385 - 440
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Illustration

271 Questions for Chapter 6: Counting

  1. A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose

    Found on Page 432

  2. Give a formula for the coefficient ofxkin the expansion of(x+1/x)100, where kis an integer.

    Found on Page 421

  3. There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot?

    Found on Page 413

  4. Show that Algorithm 1 produces the next larger permutation in lexicographic order.

    Found on Page 438

  5. What is meant by a combinatorial proof of an identity? How is such a proof different from an algebraic one?

    Found on Page 440

  6. There are \({\rm{12}}\) signs of the zodiac. How many people are needed to guarantee that at least six of these people have the same sign?

    Found on Page 440

  7. 11. How many ways are there to choose eight coins from a piggy bank containing 100 identical pennies and 80 identical nickels?

    Found on Page 432

  8. Give a formula for the coefficient ofxkin the expansion of(x2−1/x)100, where Kis an integer.

    Found on Page 421

  9. Show that Algorithm 3 produces the next larger r-combination in lexicographic order after a given r-combination.

    Found on Page 438

  10. To find the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state.

    Found on Page 405

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