Use a calculator's factorial key to evaluate each expression. (300/20)!

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Identify the expression to evaluate: $\left( \frac{300}{20} \right)!$.

Simplify the fraction inside the factorial: calculate $\frac{300}{20}$.

Once simplified, rewrite the expression as $n!$, where $n$ is the result from the previous step.

Recall that the factorial function $n!$ means the product of all positive integers from 1 up to $n$, i.e., $n! = n \times (n-1) \times (n-2) \times \cdots \times 1$.

Use a calculator's factorial key to compute the value of $n!$ based on the simplified integer $n$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Factorial Function

The factorial of a non-negative integer n, denoted n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow very quickly and are commonly used in permutations, combinations, and probability.

Order of Operations

Order of operations dictates the sequence in which parts of a mathematical expression are evaluated. In the expression (300/20)!, you first perform the division inside the parentheses, then apply the factorial to the result. This ensures accurate calculation.

Using a Calculator's Factorial Key

Many scientific calculators have a factorial function, often labeled as 'n!'. To evaluate expressions like (300/20)!, you first compute the division, then use the factorial key on the resulting integer. This simplifies calculations of large factorials.

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Textbook Question

In how many ways can five airplanes line up for departure on a runway?

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

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