Number of Triangles formed by joining N Non-Collinear Points Calculator

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✖Value of N is any natural number or positive integer that can be used for combinatorial calculations.ⓘ Value of N [n]

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✖Number of Triangles is the total count of triangles that can be formed by using a given set of collinear and non-collinear points on a plane.ⓘ Number of Triangles formed by joining N Non-Collinear Points [N_Triangles]

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Formula

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Number of Triangles formed by joining N Non-Collinear Points

Formula

`"N"_{"Triangles"} = C("n",3)`

Example

`"56"=C("8",3)`

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Number of Triangles formed by joining N Non-Collinear Points Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Triangles = C(Value of N,3)
N_Triangles = C(n,3)
This formula uses 1 Functions, 2 Variables

Functions Used

C - In combinatorics, the binomial coefficient is a way to represent the number of ways to choose a subset of objects from a larger set. It is also known as the "n choose k" tool., C(n,k)

Variables Used

Number of Triangles - Number of Triangles is the total count of triangles that can be formed by using a given set of collinear and non-collinear points on a plane.
Value of N - Value of N is any natural number or positive integer that can be used for combinatorial calculations.

STEP 1: Convert Input(s) to Base Unit

Value of N: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_Triangles = C(n,3) --> C(8,3)

Evaluating ... ...

N_Triangles = 56

STEP 3: Convert Result to Output's Unit

56 --> No Conversion Required

FINAL ANSWER

56 <-- Number of Triangles

(Calculation completed in 00.004 seconds)

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Created by Pramod Singh

Indian Institute of Technology (IIT), Guwahati

Pramod Singh has created this Calculator and 10+ more calculators!

Verified by Anirudh Singh

National Institute of Technology (NIT), Jamshedpur

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< 8 Geometric Combinatorics Calculators

Number of Rectangles in Grid

Go Number of Rectangles = C(Number of Horizontal Lines+1,2)*C(Number of Vertical Lines+1,2)

Number of Rectangles formed by Number of Horizontal and Vertical Lines

Go Number of Rectangles = C(Number of Horizontal Lines,2)*C(Number of Vertical Lines,2)

Number of Straight Lines formed by joining N Points out of which M are Collinear

Go Number of Straight Lines = C(Value of N,2)-C(Value of M,2)+1

Number of Triangles formed by joining N Points out of which M are Collinear

Go Number of Triangles = C(Value of N,3)-C(Value of M,3)

Number of Diagonals in N-Sided Polygon

Go Number of Diagonals = C(Value of N,2)-Value of N

Number of Straight Lines formed by joining N Non-Collinear Points

Go Number of Straight Lines = C(Value of N,2)

Number of Triangles formed by joining N Non-Collinear Points

Go Number of Triangles = C(Value of N,3)

Number of Chords formed by joining N Points on Circle

Go Number of Chords = C(Value of N,2)

Number of Triangles formed by joining N Non-Collinear Points Formula

Number of Triangles = C(Value of N,3)
N_Triangles = C(n,3)

What are Combinations?

In combinatorics, Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order of selection. Combinations are used to count the number of possible outcomes when the order of selection does not matter. For example, if you have a set of three elements {A, B, C}, the Combinations of size 2 would be {AB, AC, BC}. In this case, the order of the items within each combination does not matter, so {AB} and {BA} are considered the same combination.

The number of Combinations of selecting "k" items from a set of "n" items is denoted as C(n, k). It is calculated using the binomial coefficient formula: C(n, k) = n! / (k! * (n - k)!)

Combinations have various applications in mathematics, probability theory, statistics, and other fields.

What is a Triangle?

A Triangle is a three-sided polygon. It is a geometric shape that has three sides and three angles. The three angles of a Triangle always add up to 180 degrees.

The three sides of a Triangle are called the base, the height, and the hypotenuse. The three angles of a Triangle are called vertex angles.

There are three basic types of triangles:
1. Equilateral Triangles have three sides of equal length and three angles of 60 degrees.
2. Isosceles Triangles have two sides of equal length and two angles of the same measure.
3. Scalene Triangles have three sides of different lengths and three angles of different measures.

How to Calculate Number of Triangles formed by joining N Non-Collinear Points?

Number of Triangles formed by joining N Non-Collinear Points calculator uses Number of Triangles = C(Value of N,3) to calculate the Number of Triangles, Number of Triangles formed by joining N Non-Collinear Points formula is defined as the total count of triangles that can be formed by using a given set of non-collinear points on a plane. Number of Triangles is denoted by N_Triangles symbol.

How to calculate Number of Triangles formed by joining N Non-Collinear Points using this online calculator? To use this online calculator for Number of Triangles formed by joining N Non-Collinear Points, enter Value of N (n) and hit the calculate button. Here is how the Number of Triangles formed by joining N Non-Collinear Points calculation can be explained with given input values -> 35 = C(8,3).

FAQ

What is Number of Triangles formed by joining N Non-Collinear Points?

Number of Triangles formed by joining N Non-Collinear Points formula is defined as the total count of triangles that can be formed by using a given set of non-collinear points on a plane and is represented as N_Triangles = C(n,3) or Number of Triangles = C(Value of N,3). Value of N is any natural number or positive integer that can be used for combinatorial calculations.

How to calculate Number of Triangles formed by joining N Non-Collinear Points?

Number of Triangles formed by joining N Non-Collinear Points formula is defined as the total count of triangles that can be formed by using a given set of non-collinear points on a plane is calculated using Number of Triangles = C(Value of N,3). To calculate Number of Triangles formed by joining N Non-Collinear Points, you need Value of N (n). With our tool, you need to enter the respective value for Value of N and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Triangles?

In this formula, Number of Triangles uses Value of N. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of Triangles = C(Value of N,3)-C(Value of M,3)

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