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Chapter 6: Problem 79

Which of the following represent permutations? (A) An arrangement of books on a shelf (B) A group of 10 people in a bus (C) A committee of 5 senators chosen from 100 (D) A presidential cabinet of 5 portfolios chosen from 20

Short Answer

Expert verified
The scenarios (A) An arrangement of books on a shelf and (D) A presidential cabinet of 5 portfolios chosen from 20 represent permutations.

Step by step solution

01

(A) An arrangement of books on a shelf

In this scenario, the order in which the books are arranged matters, since rearranging the books would result in a different order. Thus, this represents a permutation.
02

(B) A group of 10 people in a bus

In this scenario, no specific order is mentioned for the arrangement of people in the bus. The order in which they are seated does not affect the group itself. Therefore, this does not represent a permutation.
03

(C) A committee of 5 senators chosen from 100

In this scenario, the order in which the senators are chosen does not matter. Once they are part of the committee, the order in which they were chosen is not important. Thus, this does not represent a permutation.
04

(D) A presidential cabinet of 5 portfolios chosen from 20

In this scenario, the order in which the portfolios are assigned is important, as rearranging the assignments would result in a different cabinet structure. Therefore, this represents a permutation. In conclusion, the scenarios (A) and (D) represent permutations.

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