Problem $2$:

The factorial of an integer $nin{N}_{?}1$ is the product of all the non$-$zero positive integers less than $n,$ and is denoted

by $n!.$ In other words,

$nn*(n-1)cdots2*1$

For example $44*3*2*1=24.$

Show that for all $n>3,$ we have that $2^n!$