# Thread: person who sit in a circle

1. ## person who sit in a circle

there are 7 seats around a round table, and is labelled form A to G. Find the number of ways a committee of 3 teachers and 4 parents can sit around the table?

(i ) there is no restriction
my ans is 7!=5040

(ii) all teachers must sit together
the ans is 1008. can someone explain part ii please?

2. ## Re: person who sit in a circle

Originally Posted by delso
there are 7 seats around a round table, and is labelled form A to G. Find the number of ways a committee of 3 teachers and 4 parents can sit around the table?

(i ) there is no restriction
my ans is 7!=5040

(ii) all teachers must sit together
the ans is 1008. can someone explain part ii please?
There are 7 ways to sit the group of teachers together. There are 3! ways of grouping the teachers in each case. Then in each case there are then 4! ways of seating the parents.

$7*3!*4!=1008$

3. ## Re: person who sit in a circle

in round table, any person can be taken the starting point . am i right? why we would have to times 7 in the working? in round table , the working should be (n-1)! am i right?

4. ## Re: person who sit in a circle

Originally Posted by delso
in round table, any person can be taken the starting point . am i right? why we would have to times 7 in the working? in round table , the working should be (n-1)! am i right?
The teachers can be seated in

ABC
BCD
CDE
DEF
EFG
FGA
GAB

7 ways

5. ## Re: person who sit in a circle

can i say explain in this way? since the chair is labelled from A to G (in circle), so the position of the first object placed is important. if the chairs are not labelled (in a circle), then i can ignore the 7, which means i have 3! x 4!=144

6. ## Re: person who sit in a circle

Originally Posted by delso
can i say explain in this way? since the chair is labelled from A to G (in circle), so the position of the first object placed is important. if the chairs are not labelled (in a circle), then i can ignore the 7, which means i have 3! x 4!=144
you can but it's not the problem you were given.

It clearly states the chairs are labeled.

7. ## Re: person who sit in a circle

why i cant do in this way? i have 3! arrangment for teacher, i can insert the 3 teacher in between the 4 parents. so my working is 3! x 5! =720

8. ## Re: person who sit in a circle

Originally Posted by romsek
you can but it's not the problem you were given.

It clearly states the chairs are labeled.
how if the chair is not arranged in a circle but arranged in a straight row? the working now should be 3! x5 !=720 ?? am i right? why the working isnt 3!x 4! x7 =1008 ??

9. ## Re: person who sit in a circle

Originally Posted by delso
how if the chair is not arranged in a circle but arranged in a straight row? the working now should be 3! x5 !=720 ?? am i right? why the working isnt 3!x 4! x7 =1008 ??
No that is not correct.

Your reply #7 is correct: $(3!)(5!)=720$ is correct.
There are five units the bundle of teachers and four other individuals.
So you are arranging five objects one of which, the bundle, can itself arranged in $3!$ ways.