Probability of Finding 2 Adjacent Parking Spaces for a Chevrolet

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SUMMARY

The probability of finding two adjacent parking spaces for a Chevrolet in a lot with 10 spaces and 7 already occupied is determined through combinatorial analysis. The total number of combinations of available spaces must be calculated first, followed by identifying the combinations that allow for two adjacent spaces. This involves understanding the arrangement of occupied and unoccupied spaces, leading to a definitive calculation of the probability based on the identified configurations.

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  • Combinatorial mathematics
  • Basic probability theory
  • Understanding of permutations and combinations
  • Familiarity with parking space arrangements
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  • Study combinatorial probability calculations
  • Learn about permutations and combinations in detail
  • Explore real-world applications of probability in logistics
  • Investigate similar probability problems involving spatial arrangements
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Students studying probability, mathematicians interested in combinatorial problems, and anyone involved in logistics or space optimization scenarios.

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Homework Statement


There are 10 adjacent parking places in the parking lot. When you arrive in your new Chevrolet , there are already 7 cars in the lot. What is the probability that you can find two adjacent unoccupied spaces for your Chevrolet?


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The Attempt at a Solution

 
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Posting just the one question instead of your whole assignment is an improvement, but you're still supposed to show that you've made some effort yourself. See: https://www.physicsforums.com/showthread.php?t=531087

First you need to find the total number of combinations having three available spaces out of ten. (the easy part).

Then you need to find all the combinations of ways that you can have two adjacent spaces when there are three (of 10) spaces available.
 
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