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