11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …

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Textbook Question

Chapter 8.2, Problem 17E

In Exercises #x2013;24, decide whether each exercise involves permutations or combinations, and then solve the problem.

In a club with 9 male and 11 female members, how many 5-member committees can be chosen that have

(a) all men?

(b) all women?

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Chapter 8.2, Problem 16E

Chapter 8.2, Problem 18E

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Use the Euclidean algorithm to find two sets of integers (a, b, c) such that 55a65b+143c: Solution = 1. By the Euclidean algorithm, we have: 143 = 2.65 + 13 and 65 = 5.13, so 13 = 143 – 2.65. - Also, 55 = 4.13+3, 13 = 4.3 + 1 and 3 = 3.1, so 1 = 13 — 4.3 = 13 — 4(55 – 4.13) = 17.13 – 4.55. Combining these, we have: 1 = 17(143 – 2.65) - 4.55 = −4.55 - 34.65 + 17.143, so we can take a = − −4, b = −34, c = 17. By carrying out the division algorithm in other ways, we obtain different solutions, such as 19.55 23.65 +7.143, so a = = 9, b -23, c = 7. = = how ? come [Note that 13.55 + 11.65 - 10.143 0, so we can obtain new solutions by adding multiples of this equation, or similar equations.]

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Chapter 8 Solutions

Finite Mathematics (11th Edition)

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In Exercises #x2013;24, decide whether each exercise involves permutations or combinations, and then solve the problem. In a club with 9 male and 11 female members, how many 5-member committees can be chosen that have (a) all men? (b) all women? (c) 3 men and 2 women ?

Solution Summary: The author explains that the number of possible committees of five people having all men is 126. The order in which the members are chosen is not important.

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