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In an examination, a candidate has to pass in each of the 5 subjects. In how many ways can she fail?
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As the problem states, the criterion to pass an examination is to pass in each of the 5 subjects.
The total number of possible outcomes for the entire examination is
= 32 (since there are two possible outcomes - to pass or to fail,- for each subject).
So, there are 32 possible outcomes, and there is only one outcome to pass, which is to pass in each of 5 subjects.
Thus, the number of outcomes to fail is 32-1 = 31. ANSWER
At this point, the problem is solved and explained in full.