Points A, B, C, D, and E are coplanar and no three are collinear. In how many ways can the plane be named using only these points?
To determine the number of ways the plane can be named using the given points A, B, C, D, and E, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we want to arrange the points A, B, C, D, and E to name the plane.
Since no three points are collinear, we can start by choosing any three points out of the five available to define a specific plane. After selecting three points, we can label the plane with the remaining two points in two different ways.
So, the number of ways to choose three points out of five is represented by the combination formula C(5,3), which is calculated as:
C(5,3) = 5!/(3!(5-3)!)
= 5!/3!2!
= (5 * 4)/(2 * 1)
= 10
Therefore, there are 10 ways to select three points from A, B, C, D, and E and arrange them to name the plane.