Question

Please Help
A sociology seminar has 9 members.
They begin each meeting with each member shaking hands with all the other members. No one shakes another member's hand twice. How many handshakes take place

Answer 1

Let's label all nine members, A,B,C,D,E,F,G,H,I
Now "each member shaking hands with all other memeber" simply means everybody shakes hands.

So A must shake everybody's hands:
AB
AC
AD
AE
AF
AG
AH
AI

That's 8 handshakes in total.

B must shake everybody's hand, and has already shaken A's:
BC
BD
BE
BF
BG
BG
BI

That's 7+8 handshakes in total.

And so on. The formula is \[\sum_{i=1}^{n-1}i\]
Here n=9,
So TOTAL=1+2+3+4+5+6+7+9=37

Answer 2

I understand the different combinations that were made. Would I add the number of handshakes with the total of n=9?

Answer 3

No, why would you? Think about it. The total number of handshakes is all you need.

Answer 4

Yeah I barely realized that.. sorry for asking that question. Thank You Very Much For your help I really appreciate it =)