Logistic regression can be binomial, ordinal or multinomial. Their conditional distributions are assumed to be binomial or multinomial. This sequence of polynomials is of binomial type. Induction yields another proof of the binomial theorem. Pascal's triangle determines the coefficients which arise in binomial expansions. The triangle of binomial transform coefficients is like Pascal's triangle. Many identities involving binomial coefficients can be proved by combinatorial means. The Goldschmidt method can be used with factors that allow simplifications by the binomial theorem. Khayyam was the mathematician who noticed the importance of a general binomial theorem. This formula is easiest to understand for the combinatorial interpretation of binomial coefficients. The sum of all -choose binomial coefficients is equal to . This is the probability mass function of a binomial distribution. The coefficients that appear in the binomial expansion are called binomial coefficients. The power set is closely related to the binomial theorem. As with binomial coefficients, there are several relationships between these multichoose expressions.