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There are 14 points in a plane, out of which 4 are collinear. Find the number of triangles made by these points.

A) 364
B) 360
C) 368
D) 365

Correct Answer:


B) 360

Description for Correct answer:
The required number of triangles = \( nC_3 ï¿½ mC_3 \)

Here, n =14, m = 4

= \( 14C_3 ï¿½ 4C_3 \)

=\( \large\frac{14 X 13 X 12 X 11!}{3! X 11!} - \frac{4!}{3! X 1!} \)

=\( \large\frac{14 \times 13 \times 12}{6} - \frac{4}{1} \)

=14 X 26 ï¿½ 4 = 364 ï¿½ 4 = 360

Part of solved Permutation and combination questions and answers : >> Aptitude >> Permutation and combination

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