Evaluate the expression.
$\frac{16!}{12!\cdot 4!}$

• A. 0
• B. 1
• C. 1820
• D. 43,680

Answer: (C)

Verified step by step guidance

1. Understand that a factorial, denoted by \(n!\), is the product of all positive integers from 1 up to \(n\). For example, \$5! = 5 \times 4 \times 3 \times 2 \times 1$.
2. Identify the specific factorial expressions or problems you need to work with in this practice. Since the problem is titled 'Factorials Practice 3', it likely involves simplifying or evaluating factorial expressions.
3. If the problem involves simplifying expressions with factorials, look for opportunities to cancel common factorial terms. For example, \(\frac{7!}{5!} = \frac{7 \times 6 \times 5!}{5!}\), where \$5!$ cancels out.
4. Apply the factorial definition step-by-step to expand or simplify the expressions as needed, being careful to write out the multiplication sequence clearly before canceling or combining terms.
5. After simplifying the factorial expressions, write your answer in the simplest form, either as a product or a numerical value if required.