SOLUTION: How many four-letter arrangements can be made using the letters {a, b, c, d, e} if repetitions are allowed, but no letter may follow itself?

Algebra ->  Permutations -> SOLUTION: How many four-letter arrangements can be made using the letters {a, b, c, d, e} if repetitions are allowed, but no letter may follow itself?       Log On


   

Question 943417: How many four-letter arrangements can be made using the letters {a, b, c, d, e} if repetitions are allowed, but no letter may follow itself?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1. Choose the middle (3rd) letter any of 5 ways.

2. Choose the 2nd letter any of 4 ways, (as any letter besides the letter you
   chose for the 3rd letter).

3. Choose the 1st letter any of 4 ways, (as any letter besides the letter you
   chose for the 2nd letter).

4. Choose the 4th letter any of 4 ways, (as any letter besides the letter you
   chose for the 3rd letter). 

5. Choose the 5th letter any of 4 ways, (as any letter besides the letter you
   chose for the 4th letter).

Answer = 5󫶘󫶘 = 1280

Edwin