A question paper contains five problems, each with three internal options. In how many different ways can a candidate attempt at least one problem by choosing one option per problem?

Explanation

There are 5 problems, each offering 3 choices. For each problem, a candidate can either skip it or select one of the 3 options, giving 4 possible ways per problem. Therefore, total ways are 4^5 = 1024. Since the candidate must attempt at least one problem, we exclude the case where no problems are attempted (1 way). Thus, the total number of ways is 1024 - 1 = 1023.