What is the value of the expression 5! ?

To find the value of the expression (5!), you need to understand what the notation (n!) means. The factorial of a number (n), represented as (n!), is the product of all positive integers from (1) to (n).

In this case, for (5!):

[

5! = 5 \times 4 \times 3 \times 2 \times 1

]

Calculating this step-by-step:

• First, multiply (5) by (4), which gives (20).

• Next, multiply (20) by (3), resulting in (60).

• Then, multiply (60) by (2), yielding (120).

• Finally, multiply (120) by (1), which remains (120).

Thus, (5! = 120). This correlates exactly with the choice provided, affirming that (C) is indeed the correct answer.

Understanding factorials is crucial in combinatorics and various fields of mathematics as they arise in counting problems, permutations, and in the analysis of algorithms, among other applications.