If there are 11 players in a cricket team, all of whom shake hands with each other, how many shake hands take place in the team?

Options

A. 36
B. 55
C. 66
D. none of these

Answer

To solve the problem of how many handshakes occur when all 11 players in a cricket team shake hands with each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: Each player shakes hands with every other player in the team. A handshake involves two players, so we need to count each unique pair of players.

2. **Identifying the Number of Players**: We have a total of 11 players in the team.

3. **Using the Handshake Formula**: The number of unique handshakes can be calculated using the combination formula for choosing 2 players out of n, which is given by:
\[ \text{Number of handshakes} = \binom{n}{2} = \frac{n(n-1)}{2} \]
where \( n \) is the total number of players.

4. **Substituting the Values**: Here, \( n = 11 \):
\[ \text{Number of handshakes} = \frac{11 \times (11-1)}{2} = \frac{11 \times 10}{2} \]

5. **Calculating the Result**:
\[ \frac{11 \times 10}{2} = \frac{110}{2} = 55 \]

6. **Conclusion**: Therefore, the total number of handshakes that take place in the team is **55**.

### Final Answer:
The total number of handshakes in the cricket team is **55**.

---