Question

 PLEASE HELP!!!!!!
 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?

Answer 1

If we consider the five members of one team shaking hands with each of the five members of the other team, we can simply count the number of hands the members of one team shake, since this will necessarily count all of the handshakes of the other team. Thus, as each of the five people shakes five hands, this gives  25 handshakes. There are ten basketball players total, and if each shakes hands with two referees, this gives  20 more handshakes. Thus, a total of  45 handshakes occur.

Answer 2

By taking the correspondent products, we will see that there are a total of 45 handshakes.

How many handshakes occur?

First, we only considerate the handshakes between the players, there are 5 players in each team, so the total number of handshakes here is:

5*5 = 25

Then, all of these 10 players shake hands with the 2 referees, so there are another:

2*10 = 20 handshakes.

Adding these two numbers we have:

25 + 20 = 45

We conclude that there are a total of 45 handshakes.

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