Generalized Methods to prove the Factorial and Multinomial Theorems for Machine Leaning and Cybersecurity

Combinatorial techniques with binomial coefficients, factorials and multinomial computation are used as computing algorithm or cryptographic algorithm for the programs development to apply in artificial intelligence and cybersecurity. Methodological advances in combinatorics and mathematics play a vital role in machine learning and cryptology for data analysis and artificial intelligence-based cybersecurity for protection of the computing systems, devices, networks, programs and data from cyber-attacks. In this article, combinatorial geometric series is discussed more for the application of machine learning and cybersecurity.