permutations and combinations (1 Viewer)

[nfreidman]

10 people go to a restaurant. If they sit at a circular table, find the probability of darren and samantha (2 of the people) sitting together if it is known that fred and ethel (2 others) are sitting together at the table.



thank you!

 

[bleakarcher]

10 people go to a restaurant. If they sit at a circular table, find the probability of darren and samantha (2 of the people) sitting together if it is known that fred and ethel (2 others) are sitting together at the table.



thank you!

Consider Darren and Samantha as a single element. In this element you can arrange the two people 2! ways. Place the element somewhere around the circular table to begin. Consider Fred and Ethel as another element. You can arrange Fred and Ethel 2! ways if they must sit next to one another. You now have 7 elements which you wish to arrange around the table. So the total number of arrangements such that Darren and Samantha are sitting together and Fred and Ethel are sitting together is 2!*2!*7!. Hence, the probability of this is 2!*2!*7!/9!.