The problem is to show that if $n$ is a positive integer, then $$1 = C(n, 0) < C(n, 1) < ... < C(n, \left \lfloor{ n/2} \right \rfloor) = C(n, \left \lceil {n/2} \right \rceil) > ... > C(n, n-1) > C(n, n) = 1$$.
Where $C(n, k) = \frac{n!}{k!(n-k)!}$
How can I prove the following to be equal, where n is a positive integer?
$$\frac{n!}{\left \lfloor {n/2} \right \rfloor!(n - \left \lfloor {n/2} \right \rfloor)!} = \frac{n!}{\left \lceil {n/2} \right \rceil!(n - \left \lceil {n/2} \right \rceil)!}$$