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:
The word has letters, of which are . This means the must alternate, starting from the first letter:
The remaining letters, and , must be placed in the blank spaces. There are possible letters that can go in the first space, leaving remaining letters to go in the second space, for the third space, and for the last space. Thus there are possible arrangements.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions