Problem:
In how many ways can the letters in be rearranged so that two or more do not appear together?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
First, I claim that every must be in an odd position. This is because bringing any two s together would bring them right next to each other. This means the and must each be in one of the even positions. There are choices for a letter in the second position, choices for the position for , remaining choices for a position in , remaining choices for a position in , and remaining choice for a position in . Therefore, there are possible choices.
Thus, the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions