In a plane there are 16 non collinear points find the number of straight lines formed
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I did this $^{25}C_{4}-^{7}C_{4}=12615$ quadrilaterals. But the book is giving answer $^{25}C_{4}-^{7}C_{4}-^{7}C_{3}\times ^{18}C_{1}=11985$ quadrilaterals.. I don't know what is the correct idea . I look for a short and simple way. I have studied maths up to $12$th grade. asked Sep 4, 2015 at 1:11
$\endgroup$ $\begingroup$ Your idea is very close to correct. A quadrilateral is formed by $4$ points, where at most $2$ may be colinear. Thus, we have $$ \underbrace{^{25} C_4}_{\text{ choose four points}} - \underbrace{^{7} C_4}_{\text{ subtract out ways to pick four colinear points}} - \underbrace{^{7} C_3 \cdot ^{18} C_1 }_{\text{ subtract out ways to pick three colinear points}}$$ answered Sep 4, 2015 at 1:24
Marcus MMarcus M 11k1 gold badge20 silver badges53 bronze badges $\endgroup$ 5 Free History of Indian Constitution 15 Questions 15 Marks 9 Mins Concept: To Find the Straight lines formed on 8 non collinear points We know that the straight line has two points. That is, it has starting point and ending points ∴ According to permutation and combination we have Number of lines = 8c2 Expand the above combination value. ⇒ (8×7)/(2×1) ⇒ 4× 7 ⇒ 28 lines ∴ 28 straight lines are formed from 8 non - collinear points on the X-Y plane. Latest MP Police Constable Updates Last updated on Sep 22, 2022 The Madhya Pradesh Police has released the revised schedule for the Preliminary Eligibility Test (PET) of the Madhya Pradesh Police Constable exam on 20th May 2022. The exam was cancelled in view of the extreme heatwave conditions in Madhya Pradesh. The PET is now scheduled for 6 June onwards. A total of 4000 vacancies are to be filled by the MP Police Constable Recruitment 2022. The candidates should go through the MP Police Constable Syllabus and Exam Pattern to have an idea of the requirements of the exam. Stay updated with the Quantitative Aptitude questions & answers with Testbook. Know more about Geometry and ace the concept of Lines and Angles. Answer Verified Hint: We will use the fact that 2 points form a line and then find the lines formed at max by these 10 points. After that for the b part, we will just subtract the lines which are to be ruled out because of 4 points being in a straight line and thus the answer. Complete step by step answer: Hence, the answer of part a) is 45 lines. Part b): Hence, we will get 45 – 6 + 1 lines that are 40 lines. Note: How many ways can we form a triangle using 15 non collinear points?Out of 15 points in plane, n points are in the same straight line, 445 triangles can be formed by joining these points.
How many straight lines can be drawn from non collinear points?From this, we infer that of there are n non collinear points, then every 2 points will make up a straight line and hence the number of straight lines formed is nothing but number of ways of selecting 2 points from n points = nC2.
How many straight lines can be formed from 8 non collinear points on the XY plane A 19859 B 18 C 28 D 56?∴ 28 straight lines are formed from 8 non - collinear points on the X-Y plane.
What is the formula of non collinear points?Equation of Plane Passing through 3 Non-Collinear Points
Therefore, the equation of the plane with the three non-collinear points P, Q, and R is x + 3y + 4z−9.
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