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The factorial of a number is the product of all positive integers from that number down to 1 . It plays a key role in many mathematical concepts, such as permutations, combinations, probability, and more. Explore factorial , a key math concept for counting arrangements. Learn notation, properties, special cases (0!, 1!), calculations & their applications in permutations, combinations, probability & more. Applications of Factorial The factorial formula is used in many areas, specifically in permutations and combinations of mathematics. For example, Permutations: A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order The number of ways n distinct objects can be arranged in a row is equal to n! Permutation gives the number of ways to select r elements from n elements when order matters. It is given using ...