dumpman
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Homework Statement
how many ways can 10 people sit around a roundtable if 3 particular people sit together
Homework Equations
The Attempt at a Solution
my attempt was (8-1)! x 3!
Circular Permutation problem
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how many ways can 10 people sit around a roundtable if 3 particular people sit together
my attempt was (8-1)! x 3!
Discussion
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Hi dumpman! 
Looks ok to me!
dumpman said:
Looks ok to me!
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That would only be right if you designate 3 particular seats for the 3 particular people to sit in. I think you have a number of choices for those 3 particular seats.
dumpman
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if 3 arent assigned specifically, then the answer is 10C3 x (8-1)! x 3! ?
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What you can do is think of those 3 as constituting one person. That is, find the number of different ways of seating 8 people rather than 10, then multiply by 3! for the number of ways to seat those 3 people. Oh, wait, that is (8-1)! 3!, your first answer.
Dick, that does NOT require designating "3 particular seats for the 3 particular people to sit in". Or are you suggesting we should multiply by 7!3! by 8 to allow for those 3 being anyone of the original "8" people? I don't believe that is correct.
(I could be wrong, now!)
Dick, that does NOT require designating "3 particular seats for the 3 particular people to sit in". Or are you suggesting we should multiply by 7!3! by 8 to allow for those 3 being anyone of the original "8" people? I don't believe that is correct.
(I could be wrong, now!)
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If the question means "order of seating" then I think you are right if 'right' and 'left' partners are distinguishable. If the question means "ways to seat" as in 'the chairs are numbered' then I think I'm right. It is a little ambiguous. I THINK you have to multiply 7!*3! by the number of ways to pick three consecutive chairs in a roundtable. And that's not 10C3, dumpman. They have to be adjacent. But if you think circular rotations are not important you can go with Halls and tiny-tims answer.
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all seats are equal
Yes, in my experience, "roundtable" questions always mean that the order (clockwise, say) matters, but not the actual seats …
if you're attending a dinner-party, all you're interested in is where you're sitting in relation to everyone else …
on an ordinary table, you could be stuck at the end, which is different, but on a roundtable all seats are equal.
Dick said:
Yes, in my experience, "roundtable" questions always mean that the order (clockwise, say) matters, but not the actual seats …
if you're attending a dinner-party, all you're interested in is where you're sitting in relation to everyone else …
on an ordinary table, you could be stuck at the end, which is different, but on a roundtable all seats are equal.