Question

In a group of 5 people, each shakes hands with every other person exactly once. How many handshakes occur?

• A. 10
• B. 12
• C. 15
• D. 20

Hint:

Use the combination formula $\binom{n}{2}$ for pairwise interactions like handshakes.

Answer 1

The Correct Option is A

- Step 1: Number of handshakes = $\binom{n}{2} = \frac{n(n-1)}{2}$, where $n = 5$.
- Step 2: Calculate: $\frac{5 \times 4}{2} = 10$.
- Step 3: Verify: List pairs: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5) = 10.
- Step 4: Check options: Option (1) is 10.
- Step 5: Confirm formula application.
- Step 6: Option (1) is correct.