Why is the Mean Time To Failure of multiple disks calculated via division and not multiplication?
Think of it this way. A single disk fails on average after $100,000$ hours. Now you have $100$ disks. How long before one of them fails? It will almost certainly take much less than $100,000$ hours for the first to fail, and much more than $100,000$ hours for the last to fail. (This of course depends on the distribution of failures, which is assumed to be exponential here.)

Here is another example: if you keep throwing one die, it will show $6$ after an average of $6$ throws. Now suppose that you throw two dice. How long do you expect to wait until some $6$ shows up? Certainly less than $6$ throws. (In fact, $36/11 \approx 3.27$ throws on average.)

In the second example, you need both disks to fail in order for data loss to occur. Not only this, but you also want both failure "events" to be within $10$ hours of each, since otherwise the system will recover after repairing the faulty disk. Hopefully the book explains the calculation somewhere, if not, the book is useless and you should tell your instructor to use a different one (perhaps with less pictures but more content, and not $n$th edition, prepared to finance the publisher's new yacht).