In Exercises 81–85, use a calculator's factorial key to evaluate each expression. (300/20)!

Verified step by step guidance

1. Step 1: Begin by simplifying the expression inside the factorial. Calculate \( \frac{300}{20} \).
2. Step 2: Divide 300 by 20 to simplify the expression. This will give you a whole number.
3. Step 3: Once you have the simplified number from the division, you will apply the factorial operation to this number.
4. Step 4: Use a calculator with a factorial function. Enter the simplified number and then press the factorial key (often labeled as \(!\) or \(n!\)).
5. Step 5: The calculator will compute the factorial of the number, which is the product of all positive integers up to that number.

Key Concepts

Factorial

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are commonly used in permutations, combinations, and various mathematical calculations involving sequences.

Division

Division is one of the four basic arithmetic operations, representing the process of determining how many times one number is contained within another. In the expression (300/20), the division yields 15, which is the value that will be used to calculate the factorial in the subsequent step.

Calculator Functions

Modern calculators often include a factorial function, typically denoted by an exclamation mark (!). This function allows users to compute the factorial of a number quickly and efficiently, which is particularly useful for large numbers where manual calculation would be impractical.