Factorials, Integers and Multinomial Coefficients and its Computing Techniques for Machine Learning and Cybersecurity

Mathematical and combinatorial techniques with nonnegative integers are used as computing algorithms for the programs development to apply in artificial intelligence and cybersecurity. Methodological advances in combinatorics and mathematics play a vital role in artificial intelligence and machine learning for data analysis and artificial intelligence-based cybersecurity for protection of the computing systems, devices, networks, programs and data from cyber-attacks. In connection with these ideas, this article is prepared for applications in computing science and cybersecurity. This paper presents computing and combinatorial formulae such as theorems on factorials, binomial, and multinomial coefficients and probability and binomial distributions.