Number of elements in a group

Question

The group $G$ consists of the binary strings of length $5$ under addition $\mod 2$ in each component. (It is isomorphic to $(\mathbb Z_2)^5$, the direct product of $5$ copies of $\mathbb Z_2$.)

I know the number of elements in $G$ are $32$ but how do I find it??

Answer 1

Each string is of the form _ _ _ _ _, where each of the $5$ blanks can be either $1$ or $0$. There are $2$ possibilities for the first blank, $2$ for the second, and so forth. Hence, there are $2^5$ possible binary strings.

Edit: I'm not sure I have actually answered your question. If you could elaborate on "How do I find it?", then I'll edit what I have here.