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Newbie | Next Rank: 10 Posts
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by holyxie » Fri Jun 24, 2011 7:22 pm
There are 6 groups in a room. Each group consists of 3 men. How many handshakes will there be if each man only shakes hands with people who are outside his group?
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by Frankenstein » Fri Jun 24, 2011 7:56 pm
Hi,
Let the groups be g1,g2,..,g6
Each person from g1 shakes hand with each of the other 5 groups (15 men).
So, the number of hand shakes is 3*15
Now each man from g2 shakes with each of the other 4 groups(12 men) as shakes between g2 and g1 are already counted
So, the number of hand shakes is 3*12.
Similarly for g3,g4,g5,g6
So, Total number of hand shakes is 3*(15+12+9+6+3) = 3*45 = 135
(or)
Each person from each group shakes hand with each of the other groups in 15 ways.
So, 18 men shake hands in 18*15 ways.
But we are counting each hand shake twice.
So, number of hand shakes will be 18*15/2 = 135
Cheers!

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