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)?
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
1but 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