We know that there are six people at a business convention. Let's call them A, B, C, D, E, and F. Each person shakes hands with each of the others, and we want to count the number of handshakes that will be exchanged. Notice that A will exchange a handshake with B, C, D, E, and F.
This gives us 5 handshakes so far. Next, let's consider B. We already know that this person exchanged a handshake with A. Therefore, the remaining handshakes that they will exchange is with C, D, E, and F.
This gives us another 4 handshakes that will be exchanges. Person C has already exchanged a handshake with A and B. Therefore, the remaining ones are with D, E, and F.
This is another 3 handshakes. Following the same reasoning, we can tell that the remaining handshakes of person D are with E, and F. For person E it is only a handshake with F.
This gives us the last 3 handshakes. Let's add all of them!
5 + 4 + 3 + 3 = 15
As we can see, there will be 15 handshakes exchanged at this business convention.
