Triangle of Pascal - Quantum Mechanics

Abstract This paper presents an innovative study on the sample spaces of the Cn,p experiments of Pascal’s Triangle. Currently, the only existing knowledge about these sample spaces is the formula Cn,p = n!/(n-p)!p!, which provides only the number of possible combinations obtained in these experiments. Here we present evidence of the possibility of the organization of sample spaces in these experiments. These sample spaces are organized based on their behavioral patterns, and this organization represents a mathematical model that allows us to analyze how numbers move. First, based on the theoretical development of combinatorics and probability theory, we cover simple combinations, combinations with repetition, and the Pascal’s Triangle to demonstrate how to organize the sample spaces of lotteries geometrically and according to their behavioral patterns. Then, we conduct a case study involving 6–48, which is a lottery game with 48 possible numbers among which the player chooses six; in the context of this study this lottery is a Pascal’s Triangle experiment. Based on a simple, intuitive system of color distribution, we show that expected theoretical results are in fact materialized through a historical analysis of Super Sena, a Brazilian 6–48 lottery-type discontinued in October 2001 after having produced 963 draws. Thus, the model formulates the movements of numbers randomly generated, which constitutes the platform to assess quantum information.