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How Many Triangles Can Be Obtained by Joining 12 Points, Five of Which Are Collinear? - Mathematics

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How many triangles can be obtained by joining 12 points, five of which are collinear?

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Solution

Out of 12 points, 5 points are collinear and 3 points are required to form a triangle.

\[\text{Required ways} =^{12} C_3 -^5 C_3 \]
\[ = \frac{12}{3} \times \frac{11}{2} \times \frac{10}{1} - \frac{5}{3} \times \frac{4}{2} \times \frac{3}{1} \]
\[ = 220 - 10 \]
\[ = 210\]
Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 16 | Page 16

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