<p>There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then find N.</p>
Step-by-Step Solution
Key Concept: When m points are collinear from n total points, subtract the collinear combinations from total combinations: N = C(n,3) - C(m,3).
<p><strong>Solution:</strong> When selecting 3 points from n points to form triangles, we use $\binom{n}{3}$. However, if m points are collinear, they cannot form a triangle, so we subtract $\binom{m}{3}$ from the total.</p><p>For 10 points with 6 collinear:</p><p>$$N = \binom{10}{3} - \binom{6}{3}$$</p><p>$$N = 120 - 20 = 100$$</p><p>Therefore N = 100, which satisfies N ≤ 100.</p><p>∴ Answer is (b).</p>
Correct Answer: b