Question:

Step 1: Identify the quantity to be calculated. The problem asks for an integer value, and the given answer is 120. Without the specific question, we assume the task is to calculate $5!$, which is a common value in combinatorics and often appears in integer-type questions. Step 2: Recall the definition of the factorial function. For a non-negative integer $n$, the factorial of $n$, denoted by $n!$, is the product of all positive integers less than or equal to $n$. Mathematically, this is expressed as: $$n! = n \times (n-1) \times (n-2) \times \dots \times 3 \times 2 \times 1$$ Step 3: Calculate the value of $5!$. Using the definition from Step 2, we substitute $n=5$: $$5! = 5 \times 4 \times 3 \times 2 \times 1$$ Now, we perform the multiplication: $$5! = 20 \times 3 \times 2 \times 1$$ $$5! = 60 \times 2 \times 1$$ $$5! = 120 \times 1$$ $$5! = 120$$ Step 4: State the final answer. The calculated value is 120. The final answer is $\boxed{120}$.