Discussion
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
Answer: C
For each problem the candidate has four options: attempt one of the three internal choices, or leave the problem alone.
\[ 4^{5} = 1024 \]
One of those is attempting nothing at all, which the question excludes:
\[ 1024 - 1 = 1023 \]
The 511 on offer comes from \( 2^{9} - 1 \) and ignores the internal choices.
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