word problem one---the handshake problem

[mlearner]

Hello everyone

I am currently studying a mathematics unit at a university and I have just went through some of the word problems that I need to ask a child to answer and I tried to work it out the solution before I give to the student to answer lol. I thought to share my solutions and see if everyone else has worked out the same/similar or different answers

Here is the question!!!

(a) You entered a room in which there were six other people standing. If everyone was to shake hands with every other person in the room once and only once, how many handshakes would take place?

MY answer: 20 handshakes (I drew 7 circles and drew lines to connect the two circles--without repeating it and then counted the lines)

(b) If 3 more people enter the same room and shakes hands with everyone that is already inside, how many handshakes in total would take place now?

My answer: 41 handshakes (drew 3 more circles and added lines between their circles to the other 7 circles and then added the number of lines to the 20 handshakes)

Thank you in advance for any help and suggestions!!!

Elizabeth

 

[pka]

Here is the question!!!
(a) You entered a room in which there were six other people standing. If everyone was to shake hands with every other person in the room once and only once, how many handshakes would take place?

In terms of graph theory this is equivalent to asking how many edges are in a complete graph of order seven.
$\displaystyle \dbinom{7}{2}=\dfrac{7\cdot 6}{2\cdot 1}=21$.

You must remember that between two people there is but one handshake.