Question 33574
<pre>Hi. My problem is: 
How many planes are determined by four points, no three of 
which are collinear? 
Thanks a lot!
<font size = 4><b>
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

                  <sub>4</sub>C<sub>3</sub>

and using the formula
                            n!   
                  <sub>n</sub>C<sub>r</sub> = ——————————
                        r!(n - r)!


                            4!   
                  <sub>4</sub>C<sub>3</sub> = ——————————
                        3!(4 - 3)!


                          4·3·2·1   
                  <sub>4</sub>C<sub>3</sub> = ——————————
                        3·2·1·(1)!


                          4·3·2·1   
                  <sub>4</sub>C<sub>3</sub> = ——————————
                           3·2·1

                  <sub>4</sub>C<sub>3</sub> = 4

Edwin
AnlytcPhil@aol.com</pre>