Counting the number of straight lines joining 16 points on a plane

To count the number of straight lines that can be obtained by joining 16 points on a plane, we need to use the formula:

nC2 - n

Where n is the number of points and nC2 represents the number of ways in which 2 points can be selected from n points. The subtraction of n is done to eliminate the straight lines formed by 3 or more points.

Calculating the number of straight lines

Using the formula, we get:

16C2 - 16 = 120 - 16 = 104

Therefore, the number of straight lines that can be obtained by joining 16 points on a plane is 104.

Explanation

The formula used to count the number of straight lines is based on the fact that any two points on a plane define a unique line. Therefore, the number of ways in which 2 points can be selected from n points gives us the number of unique lines that can be formed. However, we need to subtract the number of lines that are formed by 3 or more points, which is n, to get the final count of straight lines.

In this case, we have 16 points, and the number of ways in which 2 points can be selected from 16 is 16C2. This gives us 120 unique lines. However, we need to subtract the number of lines formed by 3 or more points, which is 16. Therefore, the final count of straight lines is 120 - 16 = 104.

Conclusion

In conclusion, the number of straight lines that can be obtained by joining 16 points on a plane is 104. This is calculated using the formula nC2 - n, where n is the number of points.

¹⁶C²
16x15x14!/2! (16-2!)
16x15x14!/2x14!
14! will get cut so we will be left with
16x15/2
=120
hope this helps