Question

For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) There are 10 points in a plane out of which 6 are collinear. The number of straight lines formed by joining all these points is ____.

Hint:

When multiple points are collinear, subtract the extra lines counted using \(\binom{n}{2} - 1\), where \(n\) is the number of collinear points.

Answer 1

Correct Answer: 31

Step 1: If no three points are collinear, the total number of straight lines formed by joining 10 points is: \[ \binom{10}{2} = \frac{10 \times 9}{2} = 45 \]
Step 2: Out of these 10 points, 6 points are collinear. The number of lines formed by these 6 collinear points taken two at a time is: \[ \binom{6}{2} = \frac{6 \times 5}{2} = 15 \] But all these 15 pairs lie on one single straight line. Hence, instead of 15 distinct lines, only 1 line should be counted.
Step 3: Extra lines counted due to collinearity: \[ 15 - 1 = 14 \]
Step 4: Correct number of distinct straight lines: \[ 45 - 14 = 31 \] Final Answer (up to two decimal places): \[ \boxed{31.00} \]