8 persons met on an occasion. If they shook hands with each other. One time, how many times did the hands shake?

Options

A. a)16
B. b)36
C. c)56
D. d)28

Answer

To solve the problem of how many times 8 persons shook hands with each other, we can follow these steps:

### Step 1: Understand the Problem
We have 8 persons, and each person shakes hands with every other person exactly once.

### Step 2: Calculate Total Handshakes
Each person shakes hands with 7 other persons. Therefore, if we consider all 8 persons, the total number of handshakes can be calculated as:
\[ \text{Total Handshakes} = 8 \times 7 \]

### Step 3: Adjust for Double Counting
When we calculate \(8 \times 7\), we are counting each handshake twice (once for each participant in the handshake). Therefore, we need to divide the total by 2 to get the actual number of unique handshakes:
\[ \text{Unique Handshakes} = \frac{8 \times 7}{2} \]

### Step 4: Perform the Calculation
Now, let's perform the calculations:
\[ \text{Total Handshakes} = 8 \times 7 = 56 \]
\[ \text{Unique Handshakes} = \frac{56}{2} = 28 \]

### Conclusion
Thus, the total number of unique handshakes that occurred is **28**.

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