How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points. pls po need ko na talaga.. sana merong solving. brainliest ko pag tama
Answer:
let
n be the number of points in a plane
k be the number of point to form a triangle
Step-by-step explanation:
combination of numbers
C (n, k) = n! / k(n -k)!
= 15! / 3(15 - 3)!
= 15! / 3(12)!
= (15x14x13) / (3x2)
= 2730 / 6
=455
thus there are 455 triangles
Out of 15 points in plane, n points are in the same straight line, 445 triangles can be formed by joining these points. What is the value of n?
This question was previously asked in
NDA (Held On: 18 Sept 2016) Maths Previous Year paper
View all NDA Papers >
- 3
- 4
- 5
- 6
Answer (Detailed Solution Below)
Option 3 : 5
Free
Electric charges and coulomb's law (Basic)
10 Questions 10 Marks 10 Mins
Concept:
Number of ways to select 3 points out of the n collinear points = \({\;^n}{C_3}\)
\({\;^n}{C_r}\; = \;\frac{{n!}}{{r!\left( {n\; - \;r} \right)!}}\)
Calculation:
Number of triangles that can be formed is equal to the number of ways to select 3 non-collinear points.
⇒ Number of ways to select 3 points from 15 points = 15c3
Let n points be collinear.
⇒ Number of ways to select 3 points out of the n collinear points = nc3
So, Number of ways to select 3 non-collinear points = (Number of ways to select 3 points using all the points - Number of ways to select 3 points using the collinear points)
⇒ Number of ways to select 3 non-collinear points = 15c3 - nc3
⇒ Number of triangles that can be formed = 15c3 - nc3
⇒ 445 = 15c3 - nc3
⇒ nc3 = 15c3 – 445 = 455 – 445 = 10
\(\Rightarrow \frac{{n!}}{{\left( {n - 3} \right)!\; \times 3!}} = 10\)
\(\Rightarrow \frac{{n\left( {n - 1} \right)\left( {n - 2} \right)}}{6} = 10\)
⇒ n (n – 1) (n – 2) = 60
∴ n = 5
Last updated on Sep 29, 2022
Union Public Service Commission (UPSC) has released the NDA Result II 2022 (Name Wise List) for the exam that was held on 4th September 2022. Earlier, the roll number wise list was released by the board. A total number of 400 vacancies will be filled for the UPSC NDA II 2022 exam. The selection process for the exam includes a Written Exam and SSB Interview. Candidates who get successful selection under UPSC NDA II will get a salary range between Rs. 15,600 to Rs. 39,100.
Getting Image
Please Wait...
Course
NCERT
Class 12Class 11Class 10Class 9Class 8Class 7Class 6
IIT JEE
Exam
JEE MAINSJEE ADVANCEDX BOARDSXII BOARDS
NEET
Neet Previous Year (Year Wise)Physics Previous YearChemistry Previous YearBiology Previous YearNeet All Sample PapersSample Papers BiologySample Papers PhysicsSample Papers Chemistry
Download PDF's
Class 12Class 11Class 10Class 9Class 8Class 7Class 6
Exam CornerOnline ClassQuizAsk Doubt on WhatsappSearch DoubtnutEnglish DictionaryToppers TalkBlogJEE Crash CourseAbout UsCareerDownloadGet AppTechnothlon-2019
Logout
Login
Register now for special offers
+91
Home
>
English
>
Class 11
>
Maths
>
Chapter
>
Combinatorics And Mathematical Induction
>
How many triangles can be form...
Updated On: 27-06-2022
UPLOAD PHOTO AND GET THE ANSWER NOW!
Text Solution
Answer : 455
Answer
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Related Videos
402453871
0
3.1 K
2:24
How many triangle can be formed by joining 15 points on the plane, in which on line joining any three points?
402450478
0
9.7 K
3:24
How many triangles can be formed by joining 15 points on the plane , in which no line joining any three points ?
647986285
0
3.5 K
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three point?
402450479
0
5.8 K
3:24
How many triangles can be fromed by joining 15 points on the plane , in which no line joining any three points ?
643294093
0
1.3 K
5:29
Out of 18 points in a plane, no three are in the same line except 5 points which are collinear How many triangles can be formed by joining the given points.
43959340
400
4.8 K
2:37
Twelve points are marked on a plane so that no three points are collinear. How many different triangles can be formed joining the points.
Show More
Comments
Add a public comment...
Follow Us:
Popular Chapters by Class:
Class 6
AlgebraBasic Geometrical IdeasData HandlingDecimalsFractions
Class 7
Algebraic ExpressionsComparing QuantitiesCongruence of TrianglesData HandlingExponents and Powers
Class 8
Algebraic Expressions and IdentitiesComparing QuantitiesCubes and Cube RootsData HandlingDirect and Inverse Proportions
Class 9
Areas of Parallelograms and TrianglesCirclesCoordinate GeometryHerons FormulaIntroduction to Euclids Geometry
Class 10
Areas Related to CirclesArithmetic ProgressionsCirclesCoordinate GeometryIntroduction to Trigonometry
Class 11
Binomial TheoremComplex Numbers and Quadratic EquationsConic SectionsIntroduction to Three Dimensional GeometryLimits and Derivatives
Class 12
Application of DerivativesApplication of IntegralsContinuity and DifferentiabilityDeterminantsDifferential Equations
Privacy PolicyTerms And Conditions
Disclosure PolicyContact Us