Question

A question paper consists of three sections $A,B,C$ having $6,4,3$ questions respectively. A student has the freedom to answer any number of questions but at least one question from each section is compulsory. In how many ways can the paper be attempted by the student?

• A. $5000$
• B. $8000$
• C. $6615$
• D. $9600$

Answer 1

The correct option is C

$6615$

Explanation for the correct option:

Find the number of ways of choosing one or more questions from each section:

Find the probability that out of $6,4,3$ at least one or more questions is selected.

Required Ways will be as follows.

$\begin{array}{rcl}n& =& \left(2^6-1\right)\left(2^4-1\right)\left(2^3-1\right)\\ & =& \left(64-1\right)\left(16-1\right)\left(8-1\right)\\ & =& 63·15·7\\ & =& 6615\end{array}$

Hence, option (C) is the correct answer.