The number is formed by $4,7,9,6$ according to last question. Thus, according to the first question, $6$ should be in the thousands place. From the second and last question, $7$ is in ones place, $4$ is in tens place, and $9$ is in hundreds place. 
Joy writes a four-digit number on a piece of paper and let Sandy guess.  $\textasciitilde$  Sandy asks: "Is it $$6031$$?"  Joy says: "You guess $1$ digit correct and it\textquotesingle s in the correct place."  Sandy asks: "Is it $$5672$$?"  Joy says: "You guess $2$ digits correct and they\textquotesingle re in the wrong places."  Sandy asks: "Is it $$4796$$?"  Joy says: "You guess $4$ digits correct and they\textquotesingle re in the wrong places."  $\textasciitilde$  According to the conversation above, what number does Joy write? 
Options:
  - $$4967$$ 
  - $$9764$$ 
  - $$9647$$ 
  - $$6497$$ 
  - $$6947$$ 