Question

evaluate the expression.
\\(\frac{9!}{6!}\\)
(1 point)
\\(\circ\\) 54,000
\\(\circ\\) 2!
\\(\circ\\) \\(\frac{3}{2}\\)
\\(\circ\\) 504

Explanation:

Step1: Expand factorials

By definition, \(n!=n\times(n - 1)\times\cdots\times1\). So \(9! = 9\times8\times7\times6!\).
Then \(\frac{9!}{6!}=\frac{9\times8\times7\times6!}{6!}\).

Step2: Simplify the expression

Cancel out the \(6!\) terms. We get \(9\times8\times7\).
Calculate \(9\times8\times7=(9\times8)\times7 = 72\times7=504\).

Answer:

504