What is the definition of n factorial (n!)?

What is the definition of n factorial (n!)?

• A. n + (n - 1) + (n - 2) + ... + 1
• B. n * (n-1) * (n-2) * ... * 2 * 1
• C. (n * 2) + 1
• D. n^2 + n + 1

Answer: (B)

The definition of n factorial, denoted as n!, is the product of all positive integers from n down to 1. Specifically, it is represented as n * (n - 1) * (n - 2) * ... * 2 * 1. This definition is fundamental in combinatorics and plays a crucial role in various mathematical concepts, including permutations and combinations. When calculating n!, you are effectively multiplying together every whole number that is less than or equal to n. For example, if n is 5, then 5! = 5 * 4 * 3 * 2 * 1 = 120. This operation is essential for finding the number of ways to arrange a set of n distinct objects. The other definitions listed do not align with the standard definition of factorial. Summation of integers or polynomial expressions does not describe the multiplicative process that defines factorial, which is why they are not suitable values for n!.

The definition of n factorial, denoted as n!, is the product of all positive integers from n down to 1. Specifically, it is represented as n * (n - 1) * (n - 2) * ... * 2 * 1. This definition is fundamental in combinatorics and plays a crucial role in various mathematical concepts, including permutations and combinations.

When calculating n!, you are effectively multiplying together every whole number that is less than or equal to n. For example, if n is 5, then 5! = 5 * 4 * 3 * 2 * 1 = 120. This operation is essential for finding the number of ways to arrange a set of n distinct objects.

The other definitions listed do not align with the standard definition of factorial. Summation of integers or polynomial expressions does not describe the multiplicative process that defines factorial, which is why they are not suitable values for n!.