SRL Archive - Mathematics

Fairly easy though, but I can't figure it out at this time of the day.

The Adams family consists of father, mother and four children.
Around their round table they have 6 chairs.
How many different ways can they sits, when father and mother must sit next to each other?:spot:

permutation question :)
https://www.dropbox.com/s/3ankha58ktzdmmj/table.xls
awnser = 48

I Would say: 694
Solution:
Max. solutions on 6 seats: 6*5*4*3*2*1 = 720
max solutions on 4 seats ( eliminating mom and dad ) = 4*3*2*1 = 24
720-24=694

I Hope im right :D

My answer is uncorrect, after rethinking it…

From: Enslaved
permutation question :)
https://www.dropbox.com/s/3ankha58ktzdmmj/table.xls
awnser = 48

That's indeed the correct answer. Thanks!

48 is incorrect. I'd be interested to know how you got an answer like that in the first place.

Here is one of many approaches to the question that will get you to the answer:

Picture the table or draw it out on a piece of paper - I recommend the latter.

Father and mother must be seated next to eachother.
Therefore,
With the mother sitting on the father's right side there are 6 possible ways for them to sit next to eachother like this.
There are another 6 ways in which the mother sits left to the father.

Total number of ways father/mother can sit = 12

The 4 children can also be rearranged.
Number of possible ways children can sit = 4! (4 Factorial) = 1x2x3x4 = 24

Now with every different seating the mom/dad have there are 24 options for the kids to sit.
Therefore,
12 x 24 = 288

From: Runehack123
48 is incorrect. I'd be interested to know how you got an answer like that in the first place.

Here is one of many approaches to the question that will get you to the answer:

Picture the table or draw it out on a piece of paper - I recommend the latter.

Father and mother must be seated next to eachother.
Therefore,
With the mother sitting on the father's right side there are 6 possible ways for them to sit next to eachother like this.
There are another 6 ways in which the mother sits left to the father.

Total number of ways father/mother can sit = 12

The 4 children can also be rearranged.
Number of possible ways children can sit = 4! (4 Factorial) = 1x2x3x4 = 24

Now with every different seating the mom/dad have there are 24 options for the kids to sit.
Therefore,
12 x 24 = 288

I Agree to this solution instead of 24, as Enslaved fixed Mom and Dad

its a round table silly, thought of that issue lol so instead of a combination problem, you stick 12 as the start and look for cyclical permutations

From: Enslaved
its a round table silly, thought of that issue lol so instead of a combination problem, you stick 12 as the start and look for cyclical permutations

The fact that the table is round doesn't mean every seat is exactly identical let alone our relative position to the Earth's Core when sitting on different seats. Based on a school-boy type of question where it expects you to make these types of assumptions you stand corrected. However, just because I refuse to make assumptions like this doesn't make me an idiot.

Also, since cyclic permutation implies a rearranging of values how can you even write 'instead of a combination problem' and then go on to mention cyclic permutation?

2 ways parents can sit relative to children if table is round and various other assumptions are made.
24 different ways children can rearrange themselves relative to the parents.
2x24=48
When looking at the question from a non-scientific POV.

'you stick 12 as the start' - ??? No I will not download your attached excel file - please explain…?

Well changing the position of the parents makes no.difference in the combination, sticking 12 at the start just implies when 12 is counted as both parents togetheris , @bi a OP, who is right and what is the answer?

As the question is phrased, RuneHack is correct. If the question were modified to ask how many different orders they could sit in (ignoring the absolute position of their seat) then Enslaved would be right.

I assumed that it was so as he underlined "Round" meaning that it is a significant factor in this question

From: Enslaved
Well changing the position of the parents makes no.difference in the combination, sticking 12 at the start just implies when 12 is counted as both parents togetheris , @bi a OP, who is right and what is the answer?

I don't know.I was given 4 alternatives, 48 was one of them. Don't remember more.

You're better off going with the 48. I think that's what the 'round' part is meant to imply. This has been another very nice maths discussion - keep those questions coming :) haha