STUDY GUIDE FOR PROBLEM # 20

Dania Elder

Problem 20 :

How many 5-digit ZIP codes numbers are possible if consecutive digits must be different?

  • First by¬†reading the problem you see there are 5 possible spaces to fill¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬† _¬†_ _ _ _
  • Next you see that consecutive digits must be different. Therefore you cannot have a zip code such as 11234, because the two 1’s are consecutive with one another.
  • So for the first spot you have 10 possible outcomes (0-9) as a zip code possibility.¬† 10 _ _ _ _
  • The next spot cannot be the same number as the first spot so there are 9 possible out comes

10 9 _ _ _

  • And the same for the next three spaces.

10 9 9 9 9

  • Lastly, you Multiply¬†the possible outcomes.

10*9*9*9*9 = 65,610 

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