Final answer:
In a party with eight people, each person shaking hands with every other person without repetition is a combinatorial problem, which yields 28 total handshakes. This is found through the combination formula C(8, 2), indicating there are 28 unique pairs of people shaking hands.
Step-by-step explanation:
The question concerns a scenario where eight people at a party are shaking hands with one another, and we are asked to calculate the total number of handshakes. This is a classic combinatorial problem in mathematics, which can be solved using the formula for combinations. In this case, we can imagine that one person shakes hands with the seven others. Then, the second person has already shaken hands with the first, so they only need to shake hands with six more people. This pattern continues, with each subsequent person having one less new person to shake hands with since the handshakes with prior individuals have already been counted.
The formula can be expressed as C(n, k) = n! / [k! * (n - k)!], where n is the total number of people, and k is the number we want to choose at a time. For handshakes, k equals 2, since handshakes involve two people. Therefore, we have C(8, 2) = 8! / [2! * (6!)] = (8 * 7) / (2 * 1) = 28. So, the correct answer is b. 28 handshakes in total.