PERMUTATION & COMBINATION | IIT JEE CONCEPTS | Part 10 | JEE Main 2013 | Count Number of Triangles - Videos

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In this video, we will learn an important concept of counting the number of triangles in two cases:
(i) When all the points given are non-collinear
(ii) When some of the points or a set of points are collinear

Questions Discussed
JEE Main 2013
Let Tn be the possible number of triangles formed by joining the vertices of a n-sided regular polygon. If Tn+1 – Tn = 10, then the value of n is
(A) 7 (B) 5 (C) 10 (D) 8
Answer: (B)

JEE Main 2013 Online
On sides AB, BC and AC of a triangle ABC, 3, 4, 5 distinct points (excluding vertices) are chosen. The number of triangles that can be constructed using these points as vertices are
(A) 210 (B) 205 (C) 215 (D) 220
Answer: (B)

TRY YOURSELF Questions
Question 1
Let Tn be the possible number of triangles formed by joining the vertices of a n-sided regular polygon. If Tn+1 – Tn = 21, then the value of n is
(A) 5 (B) 4 (C) 6 (D) 7
Answer: (D)

Question 2
If 7 points out of 12 lie on a single straight line, then the number of triangles formed is
(A) 19 (B) 185 (C) 201 (D) 205
Answer: (B)

Question 3
4 points out of 8 points in a plane are collinear, then the number of different quadrilateral that can be formed by joining them is
(A) 53 (B) 56 (C) 76 (D) 60
Answer (A)

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