4. If 15 people greet each other at a meeting by shaking hands with one another, how many handshakes will take place? [ 5 pts\( ] \)

When 15 people shake hands with one another, they are participating in a combination of pairs. Each handshake involves two people. The formula to calculate the total number of handshakes is given by \( \frac{n(n-1)}{2} \), where \( n \) is the total number of people. So plugging in 15, we get \( \frac{15(15-1)}{2} = \frac{15 \times 14}{2} = 105 \) handshakes. In a fun twist, imagine if every handshake was accompanied by a funny greeting or a unique dance move! Picture everyone slowly turning it into a mini dance party while keeping track of all those connections—105 handshakes turned into 105 new friendships or hilarious moments!