Question

There are 20 points in space and no 4 points are collinear.Find the number of tetrahedron formed

Answer 1

Answer:

there are 20 point in a space and no 4 Point Colony near find the number of Chitra had informed

Answer 2

Answer:

$4845$ tetrahedrons can be formed

Step-by-step explanation:

Let's clarify the concept before moving on to the answer.

Combination: Combination is the process of choosing the items from the sample; its formula is $^nC_r=\frac{n!}{r!(n-r)! }$

Where r is the number of things to be chosen from the sample, and n is the total number of items in the sample.

Given :

• 20 points in space
• No 4 points are collinear

The number of tetrahedrons can be built with 20 points in space, and no four of them being collinear; which is no four points that are not in a straight line can be in  $^{20}C_4$  ways.

There are a number of tetrahedrons that can be created where no four points are collinear are

$\implies ^{20}C_4$

$\implies \frac{20!}{4! \hspace{0.1cm} (20-4)!}$

$\implies\frac{20!}{4! \hspace{0.1cm} 16!}$

$\implies \frac{20\times19\times18\times17}{4\times3\times2\times1}$

$\implies \frac{116280}{24}$

$\implies4845$

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