Finding the digit in the units place

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Find the digit in the units place of the number $2009!+3^{7886}$.

The options available are:

  • a) $7$
  • b) $3$
  • c) $1$
  • d) $9$
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HINTS:

  • $\forall{n}\geq5:n!\equiv0\pmod{10}$
  • $\forall{n}:3^n\equiv3^{n\bmod4}\pmod{10}$