(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 ...
(Q). consider a set of two octagons, what is the maximum number of quadrilaterals that can be drawn from these 16 points ( vertices of two octagons ) as vertices such that at least one point is selected from each octagon.Solution:-⁸C₁×⁸C₃ + ⁸C₂×⁸C₂ + ⁸C₃×⁸C₁= 8×56 +...
(Q). What is the number of quadrilaterals that can be formed by joining the vertices of a polygon of n sides.Solution:-number of vertices in polygon of n sides = nHence required number of triangle = ⁿC₄ ...
(Q). How many distinct triangle can be drawn with their vertices selected from 10 points, exactly 5 of which are on one line and remaining 5 are on other parallel line?Solution:-¹⁰C₃ – ⁵C₃ – ⁵C₃= 120 – 10 – 10= 100 ...
(Q). A polygon has 65 diagonals then find its number of sides.Solution:-Let number of sides = n∴ number of vertices = n⟹ ⁿC₃ – n = 65⟹ = 65⟹ n(n-3) = 2×5×13 n(n-3) = 13(13 – 3) ∴ n = 13 ...
(Q). How many distinct triangle can be drawn with their with their vertices selected from 10 points, exactly 5 of which are collinear?Solution:-10 points could have given us ¹⁰C₃ triangles if no three of them are in a straight line, but as per question 5 of them are...
1. How many distinct lines can be drawn through 10 points, no three of which are collinear? 2. How many straight lines can be drawn through 10 points, exactly 3 of which are collinear? 3. How many distinct lines can be drawn through 10 points, 5 of which are on a...
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