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 \(n!\), means the product of all positive integers from \(n\) down to 1. For example, \$5! = 5 \times 4 \times 3 \times 2 \times 1$.
2. Identify the factorial expressions given in the problem that need to be simplified or factored.
3. Rewrite each factorial expression by expanding it into its product form to see common factors clearly. For example, \$7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$.
4. Look for common factorial terms or factors that can be canceled or factored out between expressions, such as recognizing that \$7! = 7 \times 6!$.
5. Use the properties of factorials to factor or simplify the expressions step-by-step, such as factoring out the smaller factorial or rewriting the expression in terms of factorials to simplify.