QR problems.

[sfoksn]

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How many arrangements can 6 people be seated around a circular table?

Is A is inviting 4 guests over, 2 guys and 2 girls, how many ways can A seat the guests along with himself onto a round table is no two guests of the same sex are to be seated next to each other?


Thanks.

 

[redchesus]

circular permutation is (n-1)!, so the answer to the first problem should be 5!

I have no idea for the second one...

 

[TexasOMFS]

Is A is inviting 4 guests over, 2 guys and 2 girls, how many ways can A seat the guests along with himself onto a round table is no two guests of the same sex are to be seated next to each other?

Thanks.

So if the seating arrangement is B-G-B-G-B, the two boys on the ends would be next to each other because it's a round table right? If yes, I don't see how you could get an arrangement with none of the same sex next to each other: you'd need an equal amount of boys and girls, wouldn't you?

If it is indeed NOT a round table, I'd just say 3*2*2*1*1 = 12 ways.

 

[Streetwolf]

So if the seating arrangement is B-G-B-G-B, the two boys on the ends would be next to each other because it's a round table right? If yes, I don't see how you could get an arrangement with none of the same sex next to each other: you'd need an equal amount of boys and girls, wouldn't you?

If it is indeed NOT a round table, I'd just say 3*2*2*1*1 = 12 ways.

It says no two GUESTS of the same sex... says nothing about the host. Maybe I'm just reading into it too much? Is the answer NOT 0?

 

[sfoksn]

I think since the host is on the table too, at the end the host would be separating the guests of the same sex.

I guess this question is very badly worded, if Streetwolf is confused by it too!

The answer is actually 6, but I agree with you TexasOMFS, I got 12 too. Just because you could start with the girl or the boy.

 

[TexasOMFS]

It says no two GUESTS of the same sex... says nothing about the host. Maybe I'm just reading into it too much? Is the answer NOT 0?

No you're correct, I just need to learn how to read. 🙄
Would you mind telling me how you got 0? I tried it again and came up with 4 ways. If we don't consider the host (we can just call him H), and consider the guests as G1, G2, B1, B2 (B and G for boys and girls respectively), I came up with the following combinations, in clockwise order:
1. H, G1, B1, G2, B2
2. H, G1, B2, G2, B1
3. H, G2, B1, G1, B2
4. H, G2, B2, G1, B1
Since the H position is insignificant, linearly the arrangement must be B-G-B-G. Thus 2*2*1*1? Or am I wrong?

Edit: Forgot the combinations of B-G-B-G instead of G-B-G-B:
5. H, B1, G1, B2, G2
6. H, B1, G2, B2, G1
7. H, B2, G1, B1, G2
8. H, B2, G2, B1, G1

 

[TexasOMFS]

I think since the host is on the table too, at the end the host would be separating the guests of the same sex.

I guess this question is very badly worded, if Streetwolf is confused by it too!

The answer is actually 6, but I agree with you TexasOMFS, I got 12 too. Just because you could start with the girl or the boy.

It's not badly worded, it's just a tough question with a lot of considerations to remember. Since this is a round table, the combinations are determined by the clockwise (or counterclockwise) order around the table. What you start with essentially doesn't matter, but you should start at a consistent point so you don't confuse yourself when you're thinking up the combinations. For example, using letters from my post above:
1. H, G1, B1, G2, B2
2. G1, B1, G2, B2, H
These are the same combinations on a round table, are they not?

However, I don't see why the answer is 6. Since the host doesn't matter everyone else just needs to be B-G-B-G or G-B-G-B. So 2*2*1*1 = 4. 4*2 = 8?

 

[Streetwolf]

For the record, I was asking if the answer was anything besides 0. I didn't actually go and try to solve it myself.

Edit: I see 8 ways as stated above. Do they list their ways or just the numerical answer?

 

[sfoksn]

Just numerical. It has bad explanations :/

So 8 is the correct answer?