Final answer:
The question relates to combinatorics in mathematics where ten people seated around a circular table each shake hands with every other person, resulting in 90 total handshakes.
Step-by-step explanation:
The question involves a mathematical concept known as combinatorics, which is the field of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It applies to the scenario where ten people are seated around a circular table and each person shakes hands with every other person. To calculate the total number of handshakes, we use the formula for combinations without repetition, which is C(n, k) = n! / (k!(n-k)!), where n is the total number of people and k is the number of people involved in a single handshake, which is always 2 since a handshake is between two people.
For our problem, n = 10 people and k = 2. The total number of handshakes can be calculated as:
C(10, 2) = 10! / (2!(10-2)!) = (10 × 9) / (2 × 1) = 90 handshakes.
Therefore, when ten people each shake hands with one another around a circular table, the total number of handshakes is 90.