Question 1116222: 12 points are drawn on a sheet of paper (and no three points are collinear). How many different quadrilaterals can be made?
Found 2 solutions by stanbon, KMST:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 12 points are drawn on a sheet of paper (and no three points are collinear). How many different quadrilaterals can be made?
Note:: 4 points determine the four corners of a quadrilateral.
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Ans:: 12C4 = (12*11*10*9)/(1*2*3*4) = 495
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Cheers,
Stan H.
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Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! With  points, you can form
 sets of  points.
Given points, A, B, C, and D, such that no three points are collinear,
there are  different possible ways to connect them with a closed point to point polygonal:
A-B-C-D-A,
A-B-D-C-A, and
A-C-B-D-A.
In some cases, all three polygonals will be recognized by anyone as a quadrilateral:
 ,  ,  .
In other cases, some of the polygonals may include segments intersecting each other, and may not agree with everyone's idea of a quadrilateral:
 ,  ,  .
If we can call every one of the polygonals shown above a quadrilateral,
we can form  quadrilaterals.
If crisscrossing polygonals are not considered quadrilaterals,
I suspect the number of quadrilaterals depends on the placement of the points,
and I do not know how to predict that number.
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