Final answer:
To calculate the number of handshakes among 20 people, we use the combination formula, resulting in 190 handshakes. This is done by pairing each person and ensuring no handshake is counted more than once.
Step-by-step explanation:
To find out how many handshakes there would be in a group of 20 people, where everyone shakes hands with everyone else once, we can use the formula for combination. The formula for a combination of 2 people from a group of n is given by n(n - 1) / 2. Here, n is equal to 20, so the calculation would be 20(20 - 1) / 2, which simplifies to 20 x 19 / 2. Performing the multiplication first, we get 380, and then dividing by 2, we obtain 190 handshakes.
This makes sense because the first person has 19 potential handshakes, the second person has 18 potential new handshakes (excluding the handshake with the first person which has already been counted), and so on, until the last person who has no new handshakes left (since all previous handshakes have been counted). Using this pairwise counting method ensures that no handshake is counted more than once.
Therefore, the number of handshakes that would take place is 190, which corresponds to option b.