Sample Space of Selecting 5 Balls Without Replacement

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SUMMARY

The discussion focuses on determining the sample space for selecting five balls from an urn containing six balls numbered 1-6, without replacement. The initial approach considered simultaneous selection, yielding six combinations. However, the conversation shifts to the implications of selecting the balls one at a time, prompting a deeper analysis of the resulting sample space for each combination. The conclusion emphasizes that while the methods differ, the final outcomes remain closely related.

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  • Understanding of combinatorial mathematics
  • Familiarity with the concept of sample space in probability
  • Knowledge of permutations and combinations
  • Basic principles of random experiments
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  • Study the concept of permutations in detail
  • Learn about combinations and their applications in probability
  • Explore the differences between sampling with and without replacement
  • Investigate advanced topics in probability theory, such as conditional probability
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Students of probability theory, educators teaching combinatorial concepts, and anyone interested in understanding random sampling techniques.

doozy1414
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Determine the sample space for this random experiment:

An urn contains six balls numbered 1-6. The random experiment consists of selecting five balls without replacement.

The way i did it was by figuring that the balls were selected simultaneously so i got six different combinations. But what if they are selected one at a time?
 
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If they were selected one at a time, what would the final sample space be for each possible combination? I'll give you a hint: I don't think what you did and what the answer to the problem is differs so much :)
 
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