(Q). If number of triangles that can be drawn from the given set of points as vertices is 56 then find the number of straight lines that can be drawn from these points.Solution:-Here it is given that ⁿC₃ = 56⟹ ⟹ n(n-1)(n-2) = 8×7×6∴ n = 8Hence number of straight lines...
(Q). Consider vertices of an octagon & mid point of its sides (total 16 points). How many triangles can be drawn taking these 16 points as vertices of the triangle? Solution:- Without any restriction we can get maximum ¹⁶C₃ triangles. From this we have to reduce...
(Q). Consider a square with 5 points on each side (no point on vertices)(i). How many straight lines can be drawn from these 20 points such that each line passes through exactly 2 of the given points?(ii). How many triangle can be drawn from these 20 points as...
(Q). Consider a set of 8 non-overlapping triangle in a plane such that no three points in the plane is collinear then (i). if all the possible triangle are drawn taking vertices of these triangles such that not more than 1 point is selected from a triangle then find...
(Q). Consider a polygon of ‘n’ sides. If the number of diagonal of polygon is 65 then how many triangles can be drawn from taking vertices of polygon as vertices of triangle?Solution:-number of diagonal of polygon = 65∴ ⁿC₂ – n = 65 = 65n(n-3) =...
(Q). There are two parallel lines. First line has two points A & B while second line has 10 points. How many triangle can be formed taking these 12 points as vertices of triangle?Solution:-Required number of triangles= ¹²C₃ – ¹⁰C₃= 220 – 120= 100 ...
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