There are 5 subjects in an examination. In how many ways may a student fail?

A. 16

B. 15

C. 32

D. 31

Dear student 

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