fix chapter 1 problem 11 solution

Author: michrzan

src/chapters/1/sections/counting/problems/11.tex

@@ -1,11 +1,11 @@
 \begin{enumerate}[label=(\alph*)]
-\item   Each of the $n$ inputs has $m$ choices for an output, resulting in 
+\item Each of the $n$ inputs has $m$ choices for an output, resulting in 
 $$m^{n}$$ possible functions.
 
-\item   If $n < m$, at least two inputs will be mapped to the same output, 
+\item If $n \geq m$, at least two inputs will be mapped to the same output, 
 so no one-to-one function is possible. 
 
-  If $n \geq m$, the first input has $m$ choices, the second input has $m - 1$ 
+  If $n < m$, the first input has $m$ choices, the second input has $m - 1$ 
   choices, and so on. The total number of one-to-one functions then is 
-  $$m(m-1)(m-2)\dots(m-n+1)$$
+  $$m(m-1)(m-2)\dots(m-n+1) = \frac{m!}{(m-n)!} $$
 \end{enumerate}