Four persons meet at a party. Each of them shakes hands with every other…

To determine the total number of handshakes when four people meet and each shakes hands with every other person, we can use the combination formula. Since a handshake requires two people, we are looking for the number of ways to choose 2 people from a group of 4.

Step-by-Step Calculation
The formula for the number of handshakes is:
n * (n - 1) / 2

Where n is the number of people.

Here, n = 4.

Calculation: 4 * (4 - 1) / 2 = 4 * 3 / 2 = 12 / 2 = 6.

Alternatively, you can count them person by person:

Person 1 shakes hands with 3 others (Person 2, 3, and 4).

Person 2 shakes hands with 2 others (already shook hands with Person 1).

Person 3 shakes hands with 1 other (already shook hands with Person 1 and 2).

Person 4 has already shaken hands with everyone.

Total: 3 + 2 + 1 = 6.