(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...
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