Question

In an examination a candidate has to pass in each of the papers to be successful. If the total number of ways to fail is $63,$ how many papers are there in the examination?

• A. $6$
• B. $8$
• C. $14$
• D. None of these

Answer 1

Answer: (A)

$6$

Let the number of papers be $n$.

$\therefore$ Total number of ways to fail or pass

${}^n{C}_0{+}^n{C}_1{+}^n{C}_2+...{+}^n{C}_n=2^n.$

But there is only one way to pass, i.e., when he fails in none.

$\therefore$ Total number of ways to fail $=2^n-1.$

$\therefore$ From, question $2^n-1=63\Rightarrow 2^n=64=2^6\Rightarrow n=6$