Take my word on this, or another look at Pascal's Triangle:

and don't forget the history of what is known in English as a Pascal's Triangle:

But really, it is as simple as A+B=C;
C being of the next row, and A+B being added in a 'Y' formation.

N=0
N=1
N=2
N=3
N=4
N=5
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
3
3
1
0
1
4
6
4
1
1
5
10
10
5
1
total = 1
total = 2
total = 4
total = 8
total = 16
total = 32

For such a simple structure, we won't need to examine large N-values. Also notably the terms (say X and Y) are both equal to 1, and thus drop away or collapse into unity.

Here we have the basic Combinatoric equation for Pascal’s triangle:  n-value corresponds to row and x-value to right-slanted column.

The zeros are not for decoration. I insist that the factorial of a negative number is zero. That is, unless you insist on taking absolute values simultaneously the process of taking the factorial. I don't yet understand why.

The equation for Pascal's Triangle as derived from Combinatorics is:

       N!     
X!(N-X)!

Click here to download XL file for Pascal's Triangle via Combinatorics


Any given row of Pascal's Triangle becomes a set of edge values for a Pascalloid.

And in Choice Theory, where these numbers meet in Pascal's Triangle determines the number of total possible selections of X chosen objects out of N objects.

The rest of Pascalloids incidentally expands choice theory to its logical limit and indicate story problems that are more complex than usual one-individual choice-involved decision regarding N objects.