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 and the four digits in . No character may appear in a sequence more times than it appears among the four letters in or the four digits in . A set of plates in which each possible sequence appears exactly once contains license plates. Find .
Solution:
If a sequence contains no more than one , there are sequences formed from the characters , and . If a sequence contains two 's, the 's can be placed in ways, the remaining characters can be chosen in ways, and those remaining characters can be arranged in ways, for a total of sequences. Thus , and .
The problems on this page are the property of the MAA's American Mathematics Competitions