Find the number of different straight lines obtained by joining n points on a plane, no three of which are collinear.

Options

A. `n^3`
B. `(n(n-1))/(2)`
C. `n!`
D. `2^4`

Answer

To find the number of different straight lines that can be formed by joining \( n \) points on a plane, where no three points are collinear, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to determine how many straight lines can be formed by joining \( n \) points on a plane. The condition that no three points are collinear means that any two points will uniquely determine a straight line.

2. **Choosing Points**: A straight line can be formed by selecting any two points from the \( n \) points. Therefore, the problem reduces to finding the number of ways to choose 2 points from \( n \) points.

3. **Using Combinations**: The number of ways to choose 2 points from \( n \) points is given by the combination formula:
\[ \binom{n}{2} = \frac{n!}{2!(n-2)!} \]
Here, \( n! \) (n factorial) is the product of all positive integers up to \( n \), and \( 2! \) is the factorial of 2, which equals 2.

4. **Simplifying the Combination**: We can simplify the combination formula:
\[ \binom{n}{2} = \frac{n(n-1)}{2} \]
This simplification occurs because:
- The \( n! \) in the numerator can be expressed as \( n \times (n-1) \times (n-2)! \).
- The \( (n-2)! \) in the denominator cancels out with the \( (n-2)! \) in the numerator.

5. **Final Result**: Thus, the number of different straight lines that can be formed by joining \( n \) points is:
\[ \frac{n(n-1)}{2} \]

### Conclusion:
The answer to the question is \( \frac{n(n-1)}{2} \).