Questions: You need to arrange four of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you? ways (Type a whole number.)

You need to arrange four of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you?
ways
(Type a whole number.)

Transcript text: You need to arrange four of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you? $\square$ ways (Type a whole number.)

Solution

Solution Steps

Solution

To find the number of different ways to arrange $n$ unique items along a shelf, we use the factorial function, denoted as $n!$ .

Step 1: Understanding the Problem

Given $n = 4$ unique items, we seek the total number of unique arrangements possible.

Step 2: Applying the Factorial Function

The factorial of $n$ , $n!$ , is the product of all positive integers less than or equal to $n$ . Thus, $n! = n \times (n-1) \times ... \times 1$ .

Calculation

For $n = 4$ , $n! = 24$ .

Final Answer:

The number of different ways to arrange $n = 4$ unique items along a shelf is $n! = 24$ .

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