In an examination, a student has to write exams in 8 different subjects. He is declared fail if he fails in at least one subject. The number of ways in which he can fail is

Step-by-step solution

The number of ways, in which student can fail = Number of ways, he can (fail in 1 exam + fail in 2 exams + . . .+ fail in 8 exams) aligned & = ^8 C ₁+ ^8 C ₂+ ^8 C ₃+ + ^8 C ₈ & =2^8- ^8 C ₀ & [ ^n C₀+ ^n C₁+ ^n C_n=2^n ] & =256-1=255 aligned