SOLUTION: there are 7 people at a round table with 5 seats. how many arrangements are possible? this is circular permutations of algebra 2. Please help. i don't know how to solve it. Thank

Question 1033276: there are 7 people at a round table with 5 seats. how many arrangements are possible? this is circular permutations of algebra 2.
Please help. i don't know how to solve it.
Thank you.
Tina
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.
there are 7 people at a round table with 5 seats. how many arrangements are possible? this is circular permutations of algebra 2.
Please help. i don't know how to solve it.
Thank you.
Tina
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Regarding people sitting at a round table, circular permutations differ from convectional permutations in this:

   any two permutations/arrangement of the people around the table that are obtained one from the other by "rotation" 
   in the angle around the table are considered as equivalent or indistinguishable. 

If there are n people sitting around a table, then the number of "rotations" is n (rotations by the angle , , , . . . ).

Therefore, the number of circular permutations of n objects is . =  = (n-1)!.


The number of circular permutations of n objects taken m at a time, is 

.


In your case the number of circular permutations is 

 = 7*6*4*3 = 504.


Is it your school math assignment?

If so, then it is for the first time I see such theme in the school math.

RELATED QUESTIONS
there are 7 people at a round table with 5 seats. how many arrangements are possible?... (answered by ikleyn)

Ten people are to be seated at two circular tables. One table seats six people and the... (answered by ikleyn)

The Board of Directors does not have assigned seats in the conference room. If there are... (answered by stanbon)

Seven people are arranged in a row of 3 seats. How many different arrangements are... (answered by jim_thompson5910)

THere are 10 pictures available to place on exhibit in a museum. How many arrangements... (answered by SHUgrad05)

Carlos is having dinner with his six friends. They will all be sitting at a circular... (answered by ikleyn)

there are 16 seats for passengers, how many possible seating arrangements are there for 5 (answered by Alan3354)

Use either the fundamental counting principle or the permutation formulas (or both) to... (answered by BrittanyM)

Use either the fundamental counting principle or the permutation formulas (or both) to... (answered by aswathytony)