Permutations & Combinations
Grade None
Question:
<p>The number of straight lines that can be formed by joining 20 points of which 4 points are collinear is</p>
<p style="display:inline">183</p>
<p style="display:inline">197</p>
<p style="display:inline">186</p>
<p style="display:inline">185</p>
Step-by-Step Solution
Key Concept: The number of lines is calculated by subtracting the redundant combinations of collinear points from the total combinations and adding one for the unique line they collectively form.
<p>Required number = <sup>20</sup>C<sub>2</sub> - <sup>4</sup>C<sub>2</sub> + 1<br />
= <span class="math-tex">$\frac{20 \times 19}{2}-\frac{4 \times 3}{2}$</span> + 1 = 190 - 6 + 1 = 185</p>
Correct Answer: D