1could you please say how have you solved it because this involves a hidden concept on which i intend to throw some light upon..
i am sorry if u felt bad; but i am not trying to test u
Six people sit around a circular table. In how many ways can three pairs of people shake hands so that no arms cross (nobody shakes hands with two people at the same time)?
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4 Answers
11but what do u comment upon this method :
Number the people 1,2,3,4,5,6 in a clockwise direction.
Clearly, x can't shake hands with k+2,
because then k+1 won't be able to shake kands with anybody without crossing his hand with the pair k-k+2.
If 1 shakes hands with 4 then 2-3 amd 5-6 are the other two pairs.
If 1-2 then 2-3,4-5 or 2-5,3-4.
If 1-2 then 3-4,5-6 or 3-6,4-5.
So there are five ways.
62hmm.. this is a interesting thing...
I din think this way... your method is correct..
Funnily what i did in my wrong proof is said that 1 shaking hand with 2 is different from 2 with 1 :D :P