Question

evaluate the factorial expression.
\\(\frac{20!}{17!}\\)
\\(\frac{20!}{17!}=\square\\)

Explanation:

Step1: Recall factorial definition

The factorial of a non - negative integer \(n\), denoted as \(n!\), is the product of all positive integers from \(n\) down to \(1\). So, \(n!=n\times(n - 1)\times(n - 2)\times\cdots\times1\). For \(20!\) and \(17!\), we can write \(20! = 20\times19\times18\times17!\)

Step2: Simplify the fraction

Substitute \(20! = 20\times19\times18\times17!\) into the fraction \(\frac{20!}{17!}\). We get \(\frac{20\times19\times18\times17!}{17!}\). The \(17!\) terms in the numerator and denominator cancel out, leaving us with \(20\times19\times18\)

Step3: Calculate the product

First, calculate \(20\times19 = 380\). Then, calculate \(380\times18=(400 - 20)\times18=400\times18-20\times18 = 7200-360 = 6840\)

Answer:

\(6840\)