Notes

 

Arrangements of n seats at a round table
(with rotations being equivalent)
\((n-1)! \text{ or } \displaystyle\frac{n!}{n} \)

 

 

Practice Problems

\(\textbf{1)}\) How many different ways can 5 friends sit at a round dinner table?

Show Answer

\(4!=24\) ways

 

\(\textbf{2)}\) How many different ways can 5 friends line up for a photograph?

Show Answer

\(5!=120\) ways

 

\(\textbf{3)}\) 8 coworkers sit around a table. What is the probability that you and your two best friends are sitting next to each other?

Show Answer

\(\displaystyle\frac{\left(6-1\right)!\cdot \left(3\right)!}{\left(8-1\right)!}=\displaystyle\frac{\left(5\right)!\cdot \left(3\right)!}{\left(7\right)!}=\frac{720}{5{,}040}=\frac{1}{7}\approx 14.29\%\)

 

 

See Related Pages\(\)

\(\bullet\text{ Statistics Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Probability with Marbles }\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Probability with Coin Tosses}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Probability with Dice}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Probability with Poker Hands}\)
\(\,\,\,\,\,\,\,\,\)

 

In Summary

Permutation problems involving seats around a circular table typically involve calculating the number of different arrangements of people in the seats that satisfy a certain condition. To solve these types of problems, you can use the basic principles of permutations, which involve arranging objects in a specific order. The specific approach will depend on the specific details of the problem at hand.