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?
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
