Simple combination is a type of group where the arrangements are differentiated by the nature of its elements.

Simple combination is a type of group in the study of combinatorics. The groups formed with the elements of a set are considered simple combinations are groupings of elements differentiate only by their nature.

If we consider the set B = {A, B, C, D} formed by 4 non-collinear points (which does not belong to the same line), where the amount of triangles that can form?

This is a combinatorics problem because we will form groups. In this case the group is to form triangles using 4 points not collinear. If we deploy two groups have formed: ABC and BCA, these are triangles with the same points, but in different orders which makes them equal triangles. Therefore, the groups formed in this exercise are combinations.

Simple combinations can be considered a particular kind of simple arrangement because the groups formed in arrangements are differentiated by the order and the nature of its elements. The simple combination of these different arrangements are just by nature of its elements.

Considering the above example see all the possibilities of triangles with four non-collinear points:

ABC, BAC, CAB, DAB
ABD, BAD, CAD, CAD
CBA, BCA, CBA, DBA
ACD, BCD, CBD DBC
ADB, BDA, CDA, DCA
ADC, BDC, CDB, DCB

We realize that there are several groups that differ in the order of its elements, these represent the same triangle, so we consider this exercise as a simple combination, so the amount of simple combinations that 4 points not collinear (A, B, C , D), taken 3 by 3 will form will be 4 because their groups differ by the nature of its elements and not in order.

To find this number of clusters formed on a simple combination use the following formula:
https://4.bp.blogspot.com/-xBEPBJ9VzwE/V63SXNu_UDI/AAAAAAAACos/C-mTTZV1m6YH6eu6g0wcXyk1o-NUO6qswCLcB/s1600/1.png

n is the number of elements in a set
p is a natural number less than or equal to n which is the number of elements that will form the groupings.

Replacing the above data in the formula we have:
https://2.bp.blogspot.com/-LaA5n63rPmQ/V63S876VHlI/AAAAAAAACow/e6OHsk96zRoXdzeqpQ_i5FvkfEU-OL1WgCLcB/s1600/2.png
C4,3 = 4