Perms and Combs (1 Viewer)

[ihatehippos101]

For i), say if I fixed the parents, am I still allowed to arrange them in 2! ways?
As my answer is 2!(the two parents)*2!(group of students+teachers)*4!(teachers)*5!(students) but the answer does not account for one of the 2!

 

[C2H6O]

View attachment 48546View attachment 48547
For i), say if I fixed the parents, am I still allowed to arrange them in 2! ways?
As my answer is 2!(the two parents)*2!(group of students+teachers)*4!(teachers)*5!(students) but the answer does not account for one of the 2!

Im a bit rusty so not 100% sure,
But consider that swapping the parents is already accounted for if you reverse the students and the teachers, so there is no need for the last 2! as it is already accounted for in the arrangements of the teachers and students, but yeah this is a subtlety I probably wouldn’t have picked up in the exam

 

[C2H6O]

Wait no that’s not right

 

[C2H6O]

Have you accounted for the rotational symmetry?

 

[C2H6O]

Im a bit rusty so not 100% sure,
But consider that swapping the parents is already accounted for if you reverse the students and the teachers, so there is no need for the last 2! as it is already accounted for in the arrangements of the teachers and students, but yeah this is a subtlety I probably wouldn’t have picked up in the exam

bruh sorry as you can tell I’m severely out of practise but I think this is the correct explanation. In your calculation you account for swapping the parents and swapping the student/teacher groups, but if you think about it this doubles up; imagine if you swap the parents from one position to the other, then rotate the table 180 degrees that’s the same as swapping the teachers and student groups

 

[ihatehippos101]

bruh sorry as you can tell I’m severely out of practise but I think this is the correct explanation. In your calculation you account for swapping the parents and swapping the student/teacher groups, but if you think about it this doubles up; imagine if you swap the parents from one position to the other, then rotate the table 180 degrees that’s the same as swapping the teachers and student groups

ohhhh that makes sense, thank u

 

[preptile6]

View attachment 48546View attachment 48547
For i), say if I fixed the parents, am I still allowed to arrange them in 2! ways?
As my answer is 2!(the two parents)*2!(group of students+teachers)*4!(teachers)*5!(students) but the answer does not account for one of the 2!

You fix one of the parents in FIRST. and then u put the students on 1 side and the teachers on the other. And after u do that, there is only 1 possible way to put the final parent. This is why u dont account for the factor of 2 (organising the parents). Then you apply the logic in the diagram and get 5760.