This is the question I got in Purdue University's Probability course available on YouTube:

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I don't understand they wrote 24 possible outcomes . Outcomes are just 5: 5 people in 5 seats. Mathematically, 24 is the permutation than an outcome or it is total number of events. What I am not getting here ?

  • $\begingroup$ Draw diagrams of possible seating arrangements. You should have no problem finding more than five such diagrams. If you're careful, you will find all 24 possibilities. $\endgroup$ – whuber Nov 7 '18 at 14:46

Number of sitting configurations of $n$ people around a circular table is $(n-1)!$. The way to calculate this is to first have one arbitrary person seated and treat others, i.e. $n-1$ people, as if they are seated linearly.

  • $\begingroup$ Then what is the number of events ? $\endgroup$ – Arnuld Nov 7 '18 at 8:31
  • $\begingroup$ If you could point out the exact video, I could be of more help. I only see the question in the image. Probability and combinatorics might have some sharp differences. But, if you're just asking for the how many ways these 5 people sit around the table conforming the conditions, that I can help directly. $\endgroup$ – gunes Nov 7 '18 at 8:49
  • $\begingroup$ There is no exact video. After 12 Unit 1 is over in that YouTube link question was asked. Not much helpful but that's all I can tell about it :( $\endgroup$ – Arnuld Nov 7 '18 at 9:22
  • $\begingroup$ OK. Did you understand "24 possible outcomes"? $\endgroup$ – gunes Nov 7 '18 at 9:26
  • $\begingroup$ I understand 24 is a combinatorics solution than a probability one. I understand how 5 people + 5 chairs lead to an ordered arrangement of 24. But how it applies to probability I don't understand. It is like saying we flip a coin 5 times then there are 5 outcomes. That's wrong number, outcomes are only 2, a H or T. But events (permutations) are 2^5 = 32. I don't know how to explain other than this $\endgroup$ – Arnuld Nov 7 '18 at 9:33

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