At the end of a game, each of the five members of a basketball team shake hands with each of the five members of the other team, and all of the players shake hands with the two referees. How many handshakes occur?
I want to count the total number of handshakes that happen after the game. I can break this down into two parts: the handshakes between players of different teams, and the handshakes between players and referees. For the first part, I notice that each player on one team shakes hands with each player on the other team, so that's 5 times 5, or 25 handshakes. For the second part, I notice that each player shakes hands with both referees, so that's 10 times 2, or 20 handshakes. To get the total number of handshakes, I just add these two parts: 25 plus 20, which is 45. 