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There are 5 subjects in an examination. In how many ways may a student fail? A. 16 B. 15 C. 32 D. 31

There are 5 subjects in an examination. In how many ways may a student fail? 
A. 16
B. 15
C. 32
D. 31

Grade:12th pass

2 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
possibility of being fail is given by the following result
5C5+5C4+5C3+5C2+5C1=31
Hope this helps 
Good luck 
Cheers 
Aditya Gupta
2081 Points
4 years ago
this can also be solved as follows:
consider the 5 spaces: __, __, __, __, __.
now, each space can be filled by P(pass) or F(fail).
so there are 2 ways to fill each space. so total number of ways to fill these 5 spaces= 2*2*2*2*2= 32. however, one of these ways would be – P, P, P, P, P, which is undesirable since this would mean that the student has passed. hence we need to subtract this case.
thus, total number of ways in which a student may fail= 32 – 1
= 31
kindly approve :)

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