Question 22108
YOU ONLY WANT AN ANALOGY IN GEOMETRY ..NOT THE SOLUTION TO THE PROBLEM ..OK...GOOD 
YOU CAN CONSIDER 8 PEOPLE AS 8 POINTS SO PLACED THAT  NO 3 OF WHICH ARE COLLINEAR.THAT IS NO 3 OF THEM WILL LIE ON ONE STRAIGHT LINE.NOW IF YOU TRY TO FIND THE NUMBER OF  DIFFERENT STRAIGHT LINES YOU CAN DRAW THROUGH THEM ,IT WILL BE SIMILAR TO YOUR HAND SHAKE PROBLEM.SINCE TO GET ONE STRAIGHT LINE EACH POINT (OR EACH PERSON)HAS TO BE JOINED (SHAKE HANDS) WITH EACH OTHER POINT (EACH OTHER PERSON )AND IT HAS TO BE ONLY ONCE TO GET DIFFERENT STRAIGHT LINES 9 OR DIFFERENT SHAKES).FURTHER IF A POINT A ( OR PERSON A )IS JOINED TO POINT B ( OR PERSON B )WE GET ONE LINE (ONE SHAKE HAND)AND IT IS SAME AS JOINING (SHAKING HAND )POINT B(OR PERSON B)TO POINT A (OR PERSON A)AS WE GET THE SAME LINE (OR SAME SHAKE ) WHICH IS NOT ALLOWED AS PER THE PROBLEM.SO THE 2 EXAMPLES WILL MATCH EACH OTHER EXACTLY.