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How many DIFFERENT 5-bit binary strings are there?
A$5$
B$10$
C$25$
D$32$
Answer & Solution
Correct answer: D. $32$
1. Each of the 5 positions independently has 2 choices: $0$ or $1$.
2. By the multiplication principle: $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 2^5 = 32$.
3. Same as 'how many subsets of a 5-element set' = $2^5 = 32$.
4. Other options misapply the counting.
_Source: Oscar Levin, "Discrete Mathematics: An Open Introduction", §1 (Counting — bit strings)._
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