There are 8 participants in a seminar. How many possible handshakes are there?

To find the number of possible handshakes in a seminar with 8 participants, we can use the combination formula.

In a handshake, each pair of participants shakes hands exactly once. The number of ways to choose 2 participants out of 8 to shake hands is given by the combination formula:

\[
\text{Number of handshakes} = \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28
\]

So, there are **28 possible handshakes** among the 8 participants.

Would you like more details on this calculation or have any other questions?

Here are some related questions you might find interesting:
1. How many handshakes would there be if there were 10 participants?
2. What if 2 participants refused to shake hands with anyone—how many handshakes then?
3. How does the formula change if we only want to count handshakes among a specific group, say 5 participants?
4. What would happen if each participant could shake hands multiple times with the same person?
5. How can we represent this problem using a graph theory approach?

**Tip:** The combination formula \(\binom{n}{r}\) is used to find the number of ways to choose \(r\) objects from \(n\) without regard to order. It’s widely applicable in problems involving selection and grouping.

Learn how to calculate the number of possible handshakes among 8 participants using the combination formula. Understand the principles of combinatorics and apply them to solve this problem. Suitable for students in Grades 9-12.

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