How many different strings of length $100$ may be composed of $10$ different $10$ position binary numbers?

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"How many different strings of length $100$ may be composed of $10$ different $10$ position binary numbers?"

So this series would be divided into $10$ segments of $10$ bits. Maximum number of options at one segment is $2^{10}$, my idea is that I choose $2^{10}$ for each of those segments and therefore do $10!$ to permute them, although in this case those strings wouldn't differ from each other, any idea how to solve this problem?

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There are $2^{10}$ ways to fill the first $10$ digits. Since the next ten digits must differ from the first ten digits, they can be selected in $2^{10} - 1$ ways. Can you continue?