2020 AMC 8 Problems/Problem 12
Revision as of 23:56, 17 November 2020 by Iirishabii (talk | contribs)
![$[b]Solution 1[\b]$](http://latex.artofproblemsolving.com/1/6/1/161fd2e8bcd65bfb6218149623262f198462d8d5.png)
Notice that 
= 
and we can combine the numbers to create a larger factorial. To turn 
into 
we need to multiply by 
which equals to 
Therefore, we have
![\[10!*12=12*N!.\]](http://latex.artofproblemsolving.com/b/5/7/b57d51cc68f940f63a1dde3a63bbc125429d2bfc.png)
We can cancel the 
since we are multiplying them on both sides of the equation.
We have
![\[10!=N!.\]](http://latex.artofproblemsolving.com/d/d/8/dd8b5a203f6c403ffb8a87279e697ee510eefb36.png)
From here, it is obvious that 
-iiRishabii
