Final answer:
When 8 people meet and shake hands with each other exactly once, a total of b) 28 unique handshakes will take place. This is calculated using the combinations formula C(n, r) = n! / [r!(n - r)!], which yields C(8, 2) = 28.
Step-by-step explanation:
The question asks about the number of handshakes that occur when 8 people meet and each person shakes hands with all of the other people exactly once. This can be solved using combinatorial mathematics, specifically the concept of combinations. We want to find the number of unique pairings for handshakes among a group of 8 people.
Using the formula for combinations where n is the total number of people, and we are choosing r people at a time (in this case, pairs or 2 people), the combination formula is C(n, r) = n! / [r!(n - r)!]. Here, n! denotes the factorial of n, which is the product of all positive integers up to n.
Plugging in our values, we get C(8, 2) = 8! / [2!(8 - 2)!] = (8 × 7) / (2 × 1) = 56 / 2 = 28. Therefore, 28 unique handshakes will take place.
The correct answer to the question is b. 28 handshakes occurred.