Question:
If A and B are among 20 persons who sit at random along a round table, then the probability that there are exactly six persons between A and B is:
If A and B are among 20 persons who sit at random along a round table, then the probability that there are exactly six persons between A and B is:
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When dealing with circular seating arrangements, fix one person in a seat and then arrange the remaining people accordingly.
Updated On: May 13, 2025
- \( \frac{1}{2} \)
- \( \frac{5}{16} \)
- \( \frac{2}{19} \)
- \( \frac{2}{81} \)
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The Correct Option is C
Solution and Explanation
Step 1: Calculate the total number of ways to arrange 20 people.
The total number of ways to arrange 20 people in a circle is: \[ \text{Total possible ways} = 19! \]
Step 2: Calculate the number of favorable outcomes.
For each fixed position of person A, there are 2 favorable positions for B (either 7 seats clockwise or 7 seats counterclockwise).
Step 3: Calculate the probability.
\[ P(\text{6 people between A and B}) = \frac{2}{19} \] Final Answer: \[ \boxed{\frac{2}{19}} \]
The total number of ways to arrange 20 people in a circle is: \[ \text{Total possible ways} = 19! \]
Step 2: Calculate the number of favorable outcomes.
For each fixed position of person A, there are 2 favorable positions for B (either 7 seats clockwise or 7 seats counterclockwise).
Step 3: Calculate the probability.
\[ P(\text{6 people between A and B}) = \frac{2}{19} \] Final Answer: \[ \boxed{\frac{2}{19}} \]
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