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Telephone numbers are preceded by a 3 -digit area code (e.g. 708). In the following questions, any digit from {0, 1, 2, 3, 4, 5,

Telephone numbers are preceded by a 3-digit area code (e.g. 708). In the following questions, any digit from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} can be used unless otherwise stated. How many area codes are possible if:

  1. the first digit cannot be 0 or 1, the second digit must be 1 or 7, and the third digit must be 9?
  2. the first digit must be 7 or 9, the second digit must be 0 or 1, and the third digit must not be 0?
  3. neither 0 nor 1 must be used?
  4. the first and third digits must be the same but the second must be different?

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