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Bunuel
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Each subject has two outcomes - pass or fail.

So total number of outcomes = \(2^5\)

We want the total number of ways in which the student will not pass.

The only way the student will pass, when he / she passes in all the subjects - Thus only one way.

Number of ways the student will not pass = Total - (number of ways the student will pass)

=\(2^5\) - 1

= 31 ways

IMO C
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Bunuel
In order to pass a certain examination, a student has to obtain a minimum number of marks in each of five subjects. What is the total number of ways in which the student will not pass?

(A) 5

(B) 24

(C) 31

(D) 32

(E) 120
There are two possibilities for each subject (pass or fail) and there are 5 subjects, hence total possibilities are = 2^5= 32
There is only one possibility out of 32, when the student will pass -> he has to pass in all 5 subjects.
In the other 31 possibilities, he fails.
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