9th Edition

ISBN: 9780136415893

Author: Tannenbaum

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If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Textbook Question

Chapter 4, Problem 63E

This exercise comes in two parts. Read Part I and answer (a) and (b), then read Part II and answer (c) and (d).

Part I. The Intergalactic Federation consists of three sovereign planets: Aila, with a population of 5.2 million, Balin, with a population of 15.1 million, and Cona, with a population of 10.6 million. The Intergalactic Parliament has 50 seats that are apportioned among the three planets based on their populations.

a. Find the standard divisor in the Intergalactic Parliament.

b. Find the apportionment of the 50 seats to the three planets under Hamilton's method.

Part II. Based on the results of a referendum, the federation expands to include a fourth planet, Dent, with a population of 9.5 million. To account for the additional population the number of seats in the Intergalactic Parliament is increased by 15 to a total of 65. [9.5 million individuals represent approximately 15 seats based on the standard divisor foundin (a).]

c. Find the apportionment of the 65 seats to the four planets using Hamilton's method.

d. Which paradox is illustrated by the results of (b) and (c)? Explain.

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Chapter 4, Problem 62E

Chapter 4, Problem 64E

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