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.



For such a simple structure, we won't need to examine large Nvalues. 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: nvalue corresponds to row and xvalue to rightslanted 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!(NX)!
Click here to download XL file for Pascal's Triangle via Combinatorics
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 oneindividual choiceinvolved decision regarding N objects.