EXAMPLE 1.4.5

Prior to the coin toss for a football game, the captains of the two teams meet at midfield. Team A has 4 captains, and team B has 3 captains. Each captain of team A shakes hands once with each captain of team B. Bill Gates has recently aquired the copyright on handshakes, and so he wants to know how many handshakes occur, in order to collect his royalty. How many handshakes occur?

A. 12

B. 7

C. 42

D. 49

SOLUTION

Each handshake occurs when one captain from Team A is matched with one captain from Team B. This means that if we were going to try to generate or list every handshake that occurs, in order to produce each handshake we would have to make decisions:

i. Choose a captain from Team A (4 options);

ii. Choose a captain from Team B to shake hands with the chosen captain from Team A (3 options.

According to the Fundamental Counting Principle the number of outcomes is (4)(3) =12.

The tree diagram below is presented in order to illustrate why there will be 12 handshakes.