Suppose that 9 points are distributed on a plane, such that no three points are on the same line. Form a quadrilateral by selecting the vertices from these points. How many quadrilaterals are possible?
Answers
Answer: 126
Step-by-step explanation:
Using the formula of combination
9!/(9-4)!4!= 126
= 9x8x7x6x5!/5!x4!
Reduce by removing 5!
= 9x8x7x6/4!
= 3024/4!
= 3024/24
= 126
126 quadrilaterals are possible if 9 points are distributed on a plane, such that no three points are on the same line.
Given:
9 points are distributed on a plane, such that no three points are on the same line.
To Find:
How many Quadrilaterals can be formed by selecting the vertices from given points.
Solution:
As no three points are on the same line hence any 4 points can be selected to form a Quadrilateral
4 points out of 9 points can be selected in ⁹C₄ ways as order of selection of points does not matter.
Using formula ⁿCₓ = n!/{x!(n-x)!}
Substituting n = 9 and x = 4
⁹C₄ = 9!/{4!(9-4)!}
⁹C₄ = 9!/(4!5!)
⁹C₄ = 9*8*7*6*5!/(4!5!)
⁹C₄ = 9*8*7*6*/ 4!
4! = 4 * 3 * 2 * 1 = 24
⁹C₄ = 9*8*7*6*/ 24
⁹C₄ = 9*7*2
⁹C₄ = 126
126 quadrilaterals are possible if 9 points are distributed on a plane, such that no three points are on the same line.
Learn More:
If the sides of a triangle are in the ratio 2: root 6: root 3 +1 - Brainly.in
https://brainly.in/question/11956551