<p>In a plane, there are 10 points of which 4 are collinear. How many different straight lines can be drawn joining them?</p>
Step-by-Step Solution
Key Concept: Total lines from 10 points minus overcounted lines from the 4 collinear points. Four collinear points create only 1 line, not C(4,2) lines, so we subtract the excess counting.
<p><strong>Step 1:</strong> If all 10 points were in general position (no three collinear), the number of lines would be C(10,2) = 10×9/2 = 45</p><p><strong>Step 2:</strong> However, 4 points are collinear. These 4 points are counted as C(4,2) = 6 different lines in our calculation, but they actually form only 1 line.</p><p><strong>Step 3:</strong> We must subtract the excess count: 45 - C(4,2) + 1 = 45 - 6 + 1 = 40</p><p>The '+1' accounts for adding back the single line formed by the 4 collinear points.</p><p><strong>∴ Answer: 40 different straight lines</strong></p>
Correct Answer: 40