combinatoric question about organized people in a circle

Asked Aug 22 '16 at 15:33

Active Aug 22 '16 at 17:13

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I have 12 people that arranged in a circle and 6 balls. In how many ways can I divide them for couples to play ball that no one will be disturb by the other?

In other words:All the people arranged in circle i want to draw lines between every 2 people in the circle so that there are not cut between the diagonals.

Update: I thought more about it and the solution is exactly Catalan number of N/2, this is mean the solution of this question is Catalan number of 6= 132 options.

What is a legal arrangement is on the right, and on the left an illegal arrangement:

what is legal arranged on the right, and on the left the illegal

thank you

edited Aug 22 '16 at 17:13

asked Aug 22 '16 at 15:33

Tal Shani

yes sure. All the people arranged in circle i want to draw lines between every 2 people in a circle so that there are not cut between the diagonals – Tal Shani Aug 22 '16 at 15:42
2

You want the Catalan number. See this question. – pi66 Aug 22 '16 at 15:42
@pi66 can you please be more specific with the answer. i read this answer but still didn't understand the solution. i didnt see they are using with catalan number... – Tal Shani Aug 22 '16 at 15:51
Also see this question, which is again a duplicate – Ross Millikan Aug 22 '16 at 16:28
@RossMillikan thanks but still i can't see how its helping me... – Tal Shani Aug 22 '16 at 16:34
"Don't understand" is hard to deal with. The Wikipedia article has a derivation. If you have specific questions we can help. – Ross Millikan Aug 22 '16 at 16:48

combinatoric question about organized people in a circle

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