Question

is im2a unit 5 task 22

1. simplify \\(\frac{6!}{4!}\\)

= enter your next step here

Explanation:

Step1: Recall factorial definition

The factorial of a non - negative integer \(n\), denoted as \(n!\), is defined as \(n!=n\times(n - 1)\times(n - 2)\times\cdots\times1\). So, \(6!=6\times5\times4!\) and \(4!=4\times3\times2\times1\).

Step2: Substitute factorials

Substitute \(6! = 6\times5\times4!\) into the fraction \(\frac{6!}{4!}\). We get \(\frac{6\times5\times4!}{4!}\).

Step3: Cancel out common terms

The \(4!\) terms in the numerator and the denominator cancel out (since \(\frac{4!}{4!}=1\) for \(4!
eq0\), and \(4!=24
eq0\)). So we are left with \(6\times5\).

Step4: Calculate the product

Calculate \(6\times5 = 30\).

Answer:

30