permutations??? (1 Viewer)

[Benmc]

question.
if there are 8 people in a line and two people want to stand together you go 6! * 2 * 7
if there are 8 people in a circle and two wants to sit together you just go 6! * 2
why dont you do the same for both questions?

 

[klaw]

There is no first place in a circle to fill, so a person is placed at a fixed position. So the other 7 people can then be arranged around him/her 7! ways bah... I suck at explaining

 

[jen_chik87]

hmm i duno

 

[serge]

:S......is you're working right? Shouldn't the first one be 8C2 x 7! x2!?
And the second 7! x 2!...

no, the working is right...

if anyone still has problems with this its been posted and answered twice

http://community.boredofstudies.org/showthread.php?t=90152

 

[pLuvia]

wth?

 

[word.]

question.
if there are 8 people in a line and two people want to stand together you go 6! * 2 * 7
if there are 8 people in a circle and two wants to sit together you just go 6! * 2
why dont you do the same for both questions?

well the first one, you treat the two people as a group, hence 7!, and 2! for the combinations within the two people. (6! * 7 = 7!, i have no idea why you separated it).

second one, same idea, treat two people as a group, but you minus 1 when it's a circle because you need a fixed position remember? so 6! * 2

 

[KFunk]

Think of a simple scenario of 3 people. When standing in a line the following arrangements are different:

{1, 2, 3} , {2, 3, 1} and {3, 2, 1}

however, if you put these arrangements in a circle they are identical (due to rotational symmetry) which is why you have to start of by 'putting one person in place' and arranging the others around them.