Math

QuestionA moving company delivers to two sites. What is the probability of the shortest route using the factorial rule? Calculate 2!2!.

Studdy Solution

STEP 1

Assumptions1. The moving company has to make deliveries to two different sites. . The order of the deliveries is randomly selected.
3. We are asked to find the probability that the selected order is the shortest route.
4. We are to use the factorial rule to find the number of different permutations of the two sites.

STEP 2

First, we need to understand what the factorial rule is. The factorial of a number n, denoted by n!, is the product of all positive integers less than or equal to n.
n!=n(n1)(n2)...21n! = n \cdot (n-1) \cdot (n-2) \cdot ... \cdot \cdot2 \cdot1

STEP 3

Now, we need to calculate the factorial of2, which represents the number of different permutations of the two sites.
2!=212! =2 \cdot1

STEP 4

Calculate the factorial of2.
2!=21=22! =2 \cdot1 =2So, there are2 different ways to arrange the deliveries to the two sites.

STEP 5

Since the order of the deliveries is randomly selected, each arrangement is equally likely. Therefore, the probability of selecting the shortest route is1 divided by the total number of arrangements.
Probability=1TotalnumberofarrangementsProbability = \frac{1}{Total\, number\, of\, arrangements}

STEP 6

Plug in the value for the total number of arrangements to calculate the probability.
Probability=12Probability = \frac{1}{2}The probability that the selected order is the shortest route is0.5 or50%.
Therefore, the correct answer is A. 2!=212! =2 \cdot1.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord