Question

7.4
score: 1/17 answered: 1/17
question 2
evaluate.
\\(\frac{6!}{3!}\\) =
question help: video ebook written example

Explanation:

Step1: Recall factorial definition

The factorial of a non - negative integer \(n\), denoted as \(n!\), is defined as \(n!=n\times(n - 1)\times(n - 2)\times\cdots\times1\) for \(n\geq1\) and \(0!=1\). So, \(6! = 6\times5\times4\times3\times2\times1\) and \(3! = 3\times2\times1\).

Step2: Simplify the fraction

\(\frac{6!}{3!}=\frac{6\times5\times4\times3!}{3!}\) (since \(6! = 6\times5\times4\times3!\)). Then, the \(3!\) terms in the numerator and denominator cancel out, leaving us with \(6\times5\times4\).

Step3: Calculate the product

\(6\times5\times4 = 120\).

Answer:

\(120\)