SOLUTION: Hi. My problem is: How many planes are determined by four points, no three of which are collinear? Thanks a lot!

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Question 33574: Hi. My problem is:
How many planes are determined by four points, no three of which are collinear?
Thanks a lot!
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Hi. My problem is: 
How many planes are determined by four points, no three of 
which are collinear? 
Thanks a lot!

Three noncolinear points determine a plane.

If the points are A, B, C, and D.

1. The three non-colinear points A, B, and C determine a plane.
2. The three non-colinear points A, B, and D determine a plane.
3. The three non-colinear points A, C, and D determine a plane.
4. The three non-colinear points B, C, and D determine a plane.

The answer is four.

You can also do it by the combination of 4 things taken 3 at a time

                  4C3

and using the formula
                            n!   
                  nCr = ——————————
                        r!(n - r)!


                            4!   
                  4C3 = ——————————
                        3!(4 - 3)!


                          4·3·2·1   
                  4C3 = ——————————
                        3·2·1·(1)!


                          4·3·2·1   
                  4C3 = ——————————
                           3·2·1

                  4C3 = 4

Edwin
AnlytcPhil@aol.com
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