What is 5! (5 factorial)?

To determine what 5! (5 factorial) is, we need to understand the definition of a factorial. The factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n.

So, for 5!, we calculate it as follows:

5! = 5 × 4 × 3 × 2 × 1

Now, let’s break this down step-by-step:

• Start with 5: 5
• Multiply by 4: 5 × 4 = 20
• Multiply by 3: 20 × 3 = 60
• Multiply by 2: 60 × 2 = 120
• Finally, multiply by 1 (which doesn't change the product): 120 × 1 = 120

Thus, 5! equals 120. This value represents the total number of ways to arrange 5 distinct objects, which underscores the significance of the factorial in mathematics.

The correct answer of 120 highlights your understanding of how to compute factorials, an important concept not just in mathematics but in areas like combinatorics and probability.