How might your diagram change in Example if we were counting the ways the architects could...

How might your diagram change in Example if we were counting the ways the architects could send text messages to each other? Realize now that a message sent from A to B is not the same as a message sent from B to A.

Hint: Consider putting arrowheads on the edges.

Example

Visualizing a Condition in a Word Problem

Four architects are meeting for lunch to discuss preliminary plans for a new performing arts center on your campus. Each will shake hands with all of the others. Draw a picture to illustrate this condition, and determine the number of handshakes.

SOLUTION:

We will use points labeled A, B, C, and D, respectively, to represent the people, and join these points with lines representing the handshakes, as in Figure.

If we represent the handshake between A and B by AB, then we see that there are six handshakes; namely, AB, AC, AD, BC, BD, and CD.

Figure Visualizing handshakes.