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get there are 15 points in a plane of which 10 are collinear from screen.
There are 15 points in a plane, no three of which are collinear. Find the number of triangles formed by joining them.
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There are 15 points in a plane, no three of which are collinear. Find the number of triangles formed by joining them.
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There are 15 points on a plane out of which 10 are collinear .how many triangles formed by joining these ponts?
Answer (1 of 5): Out of 15 points, we need to choose 3 points in order to make a triangle. This can be done in C(15,3) ways = 455 ways, which is equal to the number of triangles formed. But note that there are collinear points and if we choose 3 points out of those 10 collinear points, the figur...
There are 15 points on a plane out of which 10 are collinear .how many triangles formed by joining these ponts?
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5 Answers Ashish Kujur , Math-o-phile!
Answered 6 years ago · Author has 283 answers and 452.9K answer views
Originally Answered: there are 15 points on a plane out of which 10 are collinear .how many triangles formed by joining these ponts?
Out of 15 points, we need to choose 3 points in order to make a triangle. This can be done in C(15,3) ways = 455 ways, which is equal to the number of triangles formed.
But note that there are collinear points and if we choose 3 points out of those 10 collinear points, the figure would still be a straight line, not a triangle. So we need to subtract it out. Number of straight lines formed = C(10,3) = 120 lines.
Required number of triangles = 455-120 =335 triangles.
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Answered 4 years ago · Author has 928 answers and 1.6M answer views
Originally Answered: there are 15 points on a plane out of which 10 are collinear .how many triangles formed by joining these ponts?
As you know three points are needed to make a triangle,so from the given 15 points we can make
15 C 3 15C3
triangles means 455 triangles in total.
But now we have to focus on the condition that 10 points are colinear means on a straight line.
From this 10 points by choosing 3 we can make total of
10 C 3 10C3
triangles means 120 triangles.
So we will conclude that by joining them with condition we will get 455–120=335 number of triangles.
Any doubt,personal message me.
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Answered 5 years ago · Author has 58 answers and 188.1K answer views
Originally Answered: there are 15 points on a plane out of which 10 are collinear .how many triangles formed by joining these ponts?
Numbers of triangle formed by 15 point in a plane = 15C3
= 455
Number of triangle formed by 10 collinear point = 10C3
= 120 ( but these are not triangle these are lines )
So actual number of triangle formed by 15 points of which 10 are collinear is = 455 - 120
So answer is 335
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Mutyalarao Potnuru Stephen Kazoullis
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Answered 4 years ago · Author has 6.1K answers and 5.3M answer views
Originally Answered: there are 15 points on a plane out of which 10 are collinear .how many triangles formed by joining these ponts?
This means 5 are not collinear , All possible pairs of these five is 5C2.
For each of these, there are ten points to form a triangle. Answer = 5C2 x10= 100.
In addition we can form 10C2 pairs of the collinear points and connect them to the other 5 to form triangles. This gives 10C2 x 5 =45 x 5 =225
total=325.
In addition,the 5 noncollinear form 5C3 triangles.=10.
Total is 335.
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Answered 6 years ago · Author has 880 answers and 1.8M answer views
Originally Answered: there are 15 points on a plane out of which 10 are collinear .how many triangles formed by joining these ponts?
There are 15 points.Out of these 15 points 10 are collinear.Hence number of triangles formed=15 C 3-10 C 3=(15*14*13-10*9*8)/3*2*1=(2730-720)/6=2010/6=335
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[Solved] Out of 15 points in plane, n points are in the same straight
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)!
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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?
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Concept:
Number of ways to select 3 points out of the n collinear points =
nC3 nCr=n!r!(n−r)!
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
⇒n!(n−3)!×3!=10 ⇒n(n−1)(n−2)6=10
⇒ n (n – 1) (n – 2) = 60
∴ n = 5
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