binomial coefficients

Binomial coefficients are numbers that tell us how many ways we can choose a specific number of items from a larger set, regardless of the order. For example, if you have 10 books and want to select 3 to carry, the binomial coefficient indicates how many different groups of 3 you can make from the 10. These numbers appear in Pascal’s triangle and are used in probability, statistics, and algebra, especially in binomial expansions. Mathematically, they are written as "n choose k" (notated as C(n, k) or binomial coefficient n! / (k! * (n-k)!)), where “!” denotes factorial.