On a certain circle there are 10 points. What is the number of the qua

Question

On a certain circle there are 10 points. What is the number of the quadrilaterals connecting 4 points of the 10 points?

A. 80 
B. 96 
C. 180 
D. 210 
E. 240

pushpitkc · Answer

Since there are 10 points, and we can have a maximum of 4 points in a quadrilateral
The number of quadrilaterals that can be formed are 10c4

= \frac{(10*9*8*7)}{(4*3*2)} 
=210(Option D)

Nitish7 · Answer

But if all the four points are collinear then ?

pushpitkc · Answer

How can points on a circle be collinear? 
Collinear points are points which lie on a straight line!

Bunuel · Answer

On a circumference, at most two points can be collinear (endpoints of diameter).

Nitish7 · Answer

pushpitkc

Sorry my bad I mean what if all the four points on the circle are next to each other?
In that case the four points will not form a quadrilateral.
but if we do 10C4 in that case won't they be counted?

Help me understand, P&C is my weak part.

Nitish7 · Answer

pushpitkc

I see what I was missing thanks for your valuable feedback

vinsmba · Answer

There are 10points available. for a quadrilateral to be formed, we need four such points. 
so, 10C4 which is ans D. 210

MathRevolution · Answer

==> You get  10C4=\frac{(10)(9)(8)(7)}{(4)(3)(2)(1)}=210.

The answer is D. 
Answer: D

amanvermagmat · Answer

Hi

Well, on the circumference of a circle - if you draw any two points, they will always be collinear. Basically you take any two points on a circle's circumference, you will be able to join them and thus form a line, no matter how close these two points are to each other.

BUT - as soon as you take a 3rd point on the circumference, its NOT going to be collinear with BOTH the above points. This third point will obviously be collinear with the 1st point (as in you can join 1st and 3rd point to form a line) and this third point will also be collinear with the 2nd point (you can join 2nd and 3rd point to form a line) .. But this is not going to be collinear with both 1st and 2nd points at the same time. (you will not be able to form a line containing all three points)

Hope this helps.

ScottTargetTestPrep · Answer

Since there are 10 points on the circle and we need to create figures with 4 sides, the number of ways in which those figures can be created is 10C4 = 10!/  = (10 x 9 x 8 x 7)/4! = (10 x 9 x 8 x 7)/(4 x 3 x 2) = 10 x 3 x 7 = 210 ways.
 
Answer: D

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On a certain circle there are 10 points. What is the number of the qua

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