1999 AMC 8 Problems/Problem 15
Contents
Problem
Bicycle license plates in Flatville each contain three letters. The first is chosen from the set {C,H,L,P,R}, the second from {A,I,O}, and the third from {D,M,N,T}.
When Flatville needed more license plates, they added two new letters. The new letters may both be added to one set or one letter may be added to one set and one to another set. What is the largest possible number of ADDITIONAL license plates that can be made by adding two letters?
Solution
Solution 1
There are currently 
choices for the first letter, 
choices for the second letter, and 
choices for the third letter, for a total of 
license plates.
Adding 
letters to the start gives 
plates.
Adding letters to the middle gives 
plates.
Adding letters to the end gives 
plates.
Adding a letter to the start and middle gives 
plates.
Adding a letter to the start and end gives 
plates.
Adding a letter to the middle and end gives 
plates.
You can get at most 
license plates total, giving an additional 
plates, making the answer 
See Also
| 1999 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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