Given that only one of the following statement is corect, which one is correct?  ($$1$$) All of the statements below are correct.  ($$2$$) None of the statement below is corect.  ($$3$$) One of the statements above is corect.  ($$4$$) All the statements above are correct.  ($$5$$) None of the statement above is corect. 
Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis
Suppose ($$1$$) is correct, then ($$2$$) must be wrong which contradicts that only one statement is correct.  Suppose ($$2$$) is correct, then ($$5$$) is correct which contradicts that only one statement is correct.  Suppose ($$3$$) is correct, it also contradicts that only one statement is correct.  Suppose ($$4$$) is correct, it also contradicts that only one statement is correct.  Hence ($$5$$) is the correct statement. 