Breaking Into Luggage

After a few hours, David finally arrived at his hotel. When he wanted to open his briefcase; he couldn't remember the 4-digit combination code. He was, however, able to recall:

  • The \(1^\text{st} \) digit is a number between 2 and 6 inclusive.
  • The \(2^\text{nd} \) digit is a prime number between 2 and 9 inclusive.
  • The \(3^\text{rd} \) digit is a number between 5 and 8 inclusive.
  • The \(4^\text{th} \) digit is an odd number.

What is the total number of possible combination code to the briefcase?

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