Question

Express all probabilities as fractions. The United Van Lines moving company has a truck filled for deliveries to five different sites. If the order of the deliveries is randomly selected, what is the probability that it is the shortest route?

Name: Problem 16, Chapter 4: Elementary Statistics
Uploaded: 2020-10-12T17:43:17-08:00
Duration: 47 s
Channel: Harsh Gadhiya
Description: Express all probabilities as fractions. The United Van Lines moving company has a truck filled for deliveries to five different sites. If the order of the deliveries is randomly selected, what is the probability that it is the shortest route?

   Express all probabilities as fractions.
The United Van Lines moving company has a truck filled for deliveries to five different sites. If the order of the deliveries is randomly selected, what is the probability that it is the shortest route?

Elementary Statistics

Mario F. Triola 13th Edition

Chapter 4, Problem 16

Instant Answer

Solved by Expert Harsh Gadhiya

10/12/2020

Step 1

Since the order of deliveries matters, we can use the concept of permutations. For 5 different sites, the total number of permutations is 5 factorial (5!). Show more…

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Express all probabilities as fractions. The United Van Lines moving company has a truck filled for deliveries to five different sites. If the order of the deliveries is randomly selected, what is the probability that it is the shortest route?

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Key Concepts

Probability

Probability is the measure of the likelihood that a particular event will occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In problems involving random permutations, probability helps assess the chance of a specific ordering, such as the one corresponding to the shortest route.

Permutations

Permutations refer to the different arrangements or orders in which a set of items can be organized. This concept is crucial for understanding the total number of possible sequences that can occur, such as the total different orderings of delivery sites.

Factorials

Factorials are mathematical operations used to compute the number of permutations. The factorial of a positive integer n (denoted as n!) is the product of all positive integers up to n. It is essential for determining how many distinct arrangements are possible for a given number of items.

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