2007 AIME II Problems/Problem 1
Problem
A mathematical organization is producing a set of commemorative license plates. Each plate contains a sequence of five characters chosen from the four letters in AIME and the four digits in 2007. No character may appear in a sequence more times than it appears among the four letters in AIME or the four digits in 2007. A set of plates in which each possible sequence appears exactly once contains N license plates. Find N/.
Solution
There are 7 different characters that can be picked, with 0 being the only number that can be repeated twice.
- If appears 0 or 1 times amongst the sequence, there are sequences possible.
- If appears twice in the sequence, there are places to place the s. There are ways to place the remaining three characters. Totally, that gives us .
Thus, , and .
See also
2007 AIME II (Problems • Answer Key • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.