I wonder if someone could give me the formula - or better still the answer to this.
I want to figure out how many different configurations I could get from 2 colors or symbols (Red/Black)varranged in sequences of five. repeating colors is ok. So for example
red red black black red red black red black black black black red red red
etc.
I'd really just like an answer :)
Arranged in sequences of $5$ makes no difference, it is all just a long "word" in the letters R and B.
There are $2$ words of length $1$.
Every word of length $1$ can be extended (on the right) in $2$ ways to make a word of length $2$. So there are $4$ words of length $2$.
Every word of length $2$ can be extended in $2$ ways to make a word of length $3$. So there are $8$ words of length $3$.
Similarly, there are $16$ words of length $4$, $32$ words of length $5$, and so on.
There are $2^n$ words of length $n$.
