$5$ students $A$, $B$, $C$, $D$ and $E$ went to visit their form teacher Ms Fan on Teachers\textquotesingle{} Day. Before that, they were trying to guess the $3-$digit block number of Ms Fan\textquotesingle s place and made the following statements.  Student $A$: The number is a multiple of $27$.  Student $B$: The number is a muitiple of $7$.  Student $C$: The sum of the digits of the number is $17$.  Student $D$: The number is a perfect square.  Student $E$: The number is a factor of $89100$.  Ms Fan told them that only three of these statements are true. What is the $3-$digit block number of Ms Fan\textquotesingle s place? 
Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations