The number of straight lines can be formed by joining 12points ,7 of which are collinear
Answers
Answer:
5 are not collinear
Step-by-step explanation:
Because 7 are collinear from 12
Answer:
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Rejitha Krishnan RG
Oct 24, 2014
How many straight lines and how manytriangles can be obtained by joining 12 points,5 of which are collinear?
a)how many straight lines can be obtained by joining 12 points,5 of which are collinear? b)how many triangles can be obtained by joining 12 points,5 of which are collinear?
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Raghunath Reddy
Sol:a) A straight line can be obtained by joining any two points. 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 12C2 - 5C2 +1 . = 66 - 10 +1 = 57. b) Total 12 points, 5 are collinear, 7 are non collinear. 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.