Sol:a) Show
Given 12 points,5 of which are collinear. In this case the number of straight lines that can be formed using the 5 collinear points is only 1. The number of straight lines when 5 of the 12 points are collinear is given by To solve this, find out all the ways three points can be joined to form a triangle. Case 1 - All three points selected from the 7 non-collinear points. This can be done in 7C3 ways. = 35 ways. Case 2 - Two points are selected from the 7 non-collinear points, and one from the 5 collinear points.This can be done in 7C2 x 5C1 ways. = 21 x 5 = 105 ways. Case 3 - One point is selected from the 7 non-collinear points and two points are selected from the 5 collinear points. This can be done in 7C1 x 5C2 ways. = 7 x 10 = 70 ways. Case 4 - zero points from the 7 non-collinear points and three from the 5 collinear points. This case will not yield a traingle and only yield straight lines. So it will 0. Hence answer is where case 1 or case 2 or case 3 happens to form a valid triangle, i.e. 35 + 105 + 70 = 210 ways. Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Solution The correct option is C185The number of ways of selecting 3 points out of 12 points is 12C3. The number of ways of selecting 3 points out of 7 points on the same straight line is 7C3. Hence the number of triangles formed will be 12C3−7C3=185.Solve Textbooks Question Papers How many state lines triangles can be formed by joining 12 point 7 of which are the same line?Hence the number of triangles formed will be 12C3−7C3=185.
How many triangles can be formed by joining 12 points out of which 7 are collinear justify?How many triangles can be formed by joining 12 points, 7 of which are collinear? The number of triangles that can be formed from 12 points is = 10 as 7 points are collinear. E is the answer.
How many straight lines can be formed by joining 12 points?=6C1×6C1+6C2+1=52.
How many triangles can be formed by joining 12 points 4 of which are collinear?Solution : Number of triangles `=(. ^(12)C_(3)-. ^(4)C_(3))=(220-4)=216`.
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