Number of lines, which can be drawn through 6 points on a circle is 15.

Answer

To solve the problem of finding the number of lines that can be drawn through 6 points on a circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the number of lines that can be formed using 6 points that lie on the circumference of a circle.

2. **Identifying the Requirement**: To form a line, we need at least 2 points. Therefore, we need to select 2 points from the 6 points available.

3. **Using Combinations**: The number of ways to choose 2 points from 6 can be calculated using the combination formula, which is denoted as \( C(n, r) \) or \( nCr \). Here, \( n \) is the total number of points (6) and \( r \) is the number of points to choose (2). So, we need to calculate \( C(6, 2) \).

4. **Applying the Combination Formula**: The formula for combinations is given by:
\[ C(n, r) = \frac{n!}{r!(n-r)!} \]
Substituting \( n = 6 \) and \( r = 2 \):
\[ C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2! \cdot 4!} \]

5. **Calculating Factorials**:
- \( 6! = 6 \times 5 \times 4! \)
- \( 2! = 2 \times 1 = 2 \)
- \( 4! \) cancels out in the numerator and denominator.

6. **Simplifying the Expression**:
\[ C(6, 2) = \frac{6 \times 5 \times 4!}{2! \times 4!} = \frac{6 \times 5}{2} = \frac{30}{2} = 15 \]

7. **Conclusion**: Therefore, the number of lines that can be drawn through 6 points on a circle is \( 15 \).

### Final Answer:
The number of lines that can be drawn through 6 points on a circle is **15**.

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