The number of straight lines that can be formed by joining 20 points o...
Solution:
To find the number of straight lines that can be formed by joining 20 points, we need to consider two cases:
1. When no three points are collinear
2. When four points are collinear
Case 1: When no three points are collinear
When no three points are collinear, any two points can be joined to form a straight line.
The number of ways to select 2 points out of 20 is given by the combination formula C(20, 2) which is equal to (20!)/(2!(20-2)!) = 190.
But we have to subtract the number of lines which are formed by joining collinear points.
Case 2: When four points are collinear
When four points are collinear, we can only consider one line instead of four lines.
The number of ways to select 4 points out of 20 is given by the combination formula C(20, 4) which is equal to (20!)/(4!(20-4)!) = 4845.
However, we need to subtract the number of lines formed by joining the collinear points.
Since there are four collinear points, the number of lines formed by joining them is 1.
Therefore, the total number of lines formed by joining the 20 points when four points are collinear is 4845 - 1 = 4844.
Calculation:
In case 1, we have 190 lines, and in case 2, we have 4844 lines formed by joining the points.
So, the total number of lines formed is 190 + 4844 = 5034.
However, we have counted each line twice (once in each case), so we need to divide the total by 2.
Therefore, the final answer is 5034/2 = 2517.
But in the options given, none of them matches with this answer.
Hence, the answer provided in the question is incorrect or the options provided are incorrect.
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