can sumone answer this question plz (1 Viewer)

[jen_chik87]

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]

http://community.boredofstudies.org/showthread.php?t=90141

 

[Stefano]

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?

Because if we have them arranged in a line there is a fixed FIRST and LAST position. If they are then joined into a circle we don't know who was last/first.

So; (#ways the 2ppl can arrange themselves)(#ways the others can arrange themselves)(#ways the two groups can arrange themselves)

Line: 2!6!(7-1)!
Circle: 2!6!(7-7)!

(Since if you spin the table or look at it from a different perspective it's the same thing)

Does that make sense?

 

[Will Hunting]

Treating the pair as a single person, there are 7 people in total.

Now, in both cases, there are 2! different arrangements of the pair.

But, with the line, each position the pair can be in is distinct.

(eg. AB123456 is different to 456AB123)

But, with the circle, the positions only become distinct after you've fixed someone somewhere. Otherwise, the positions are not distinct.

(eg. AB123456 is the same as 456AB123 until you say that AB occupies a certain two seats, at which point the remaining 6 can be arranged in 6! different ways).

Using the product rule of probability for successive events,

There are 2!.7.6! different arrangements for the line.

And 2!.6! different arrangements for the circle.

 

[jen_chik87]

thanx guys its making a bit more sense now