There are 26 letters in the alphabet. How many 5-letter words can you make if you can repeat letters, but cannot have two letters in a row that are the same?
My strategy:
Since there are 26 letters, the words can be made by $26 . 25. 24. 25. 26$. Is this true? I have a feeling a erred somewhere.
Best Answer
Let's break it down.
The first letter obviously has 26 choices. The second letter can be any of the letters, minus the previous one, so 25 choices. The third letter can be anything except the second letter, so 25 choices, and likewise for every other letter.
Thus the number of n-length words of this type is $26\times25^{n-1}$, or in this case:
$26\times25^{4} = 10156250$.