Answer
2046 bit strings
Work Step by Step
Product rule states that if one event can occur in m ways and second event can occur in n ways then the two events can occur in sequence in m.n ways
Sum rule states that if an event can occur in either m ways or in n ways (not overlapping), the number of ways the event can occur is m+n.
We use the product rule to determine the number of bits strings with length n,
and we use sum rule as there are $2^{n}$ bits of length n for each n from 1 to 10.
So we get 2 + $2^{2}$ +...$2^{10}$ = 2046
