In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament?

Explanation

To solve the problem of how many matches will be played in a chess tournament with six players where each player plays every other player exactly once, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Number of Players**:
- We have a total of \( n = 6 \) players in the tournament.

2. **Understanding Pairing**:
- Each match is played between two players. Therefore, we need to determine how many unique pairs of players can be formed from the six players.

3. **Using Combinatorial Formula**:
- The number of ways to choose 2 players from \( n \) players can be calculated using the combination formula:
\[ \text{Number of matches} = \binom{n}{2} = \frac{n(n-1)}{2} \]
- Here, \( n(n-1) \) represents the total ways to pair players, and we divide by 2 to account for the fact that the order of selection does not matter (i.e., choosing player A and player B is the same as choosing player B and player A).

4. **Substituting the Value of n**:
- Substitute \( n = 6 \) into the formula:
\[ \text{Number of matches} = \frac{6(6-1)}{2} = \frac{6 \times 5}{2} \]

5. **Calculating the Result**:
- Calculate the multiplication:
\[ 6 \times 5 = 30 \]
- Now divide by 2:
\[ \frac{30}{2} = 15 \]

6. **Conclusion**:
- Therefore, the total number of matches that will be played during the tournament is **15**.