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Apologies in advance for lack of knowledge in how to ask this!

I have a linear story with multiple options. Think of it as a choose your own adventure book.

You start at A, then you have to choose whether to go to AA or AB.

This process repeats with whatever option you choose- 2 choices at each step.

In total, you’ll go through 4 choices- so your last choice will land you at (example) AAAAA

My question is, how would I calculate how many ways there are to read the story? Remember it’s linear, so there’s no going back, and there are only 2 choices every step of the way (example) A or B.

Please remember I might not know mathematics terms so please help me understand! Thank you in advance!

Taytee13
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    Each time you make a choice, you're basically multiplying the number of paths by $2$, since you can have a path where you choose one way or the other. So that gives $2 \times 2 \times 2 \times 2$ total paths. If you know binary, when you list all your paths (in your ABBAB notation) it'll look like the numbers from $0$ to $15$ in binary if you think of $A$ as $0$ and $B$ as $1$. – Izaak van Dongen Jan 19 '20 at 15:55

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First, notice that for each choice you have two different possibilities $A$ and $B$. Let $C_n$ the number of diferent ways of reading $n$ long story. So, I have that: $$C_n=2^n$$ when $n=1$ you have two chores and if you use $4$ you get $C_4=2^4=16$.

Matteo
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