Question

In an examination a candidate is required to pass in 4 different subjects in how many ways he can fail

Answer 1

No. of ways in which one can pass or fail in the examination = 2 to the power 4=16

To pass one has to pass in all the subjects.= 1 way

∴ The no. of ways in which one can fail = 16-1=15 ways.

Answer 2

The no. of ways a student can fail the exam is equal to 15.

If the no. Of exams are equal to 4 , then a student has to pass in all the exams to pass .

No. Of ways a student can fail = fails in one subject + fail in 2 subjects + fail in three subjects + fail in 4 subjects

=> 4!/3! + 4!/2!2! +4!/3! + 1

=> 4+6+4+1

=>15

The no. Of ways a student can fail = 15