Question

A question paper consists of two sections having respectively 3 and 4 questions. The following note is given on the paper "It is not necessary to attempt all the questions. One question from each section is compulsory". In how many ways can a candidate select the questions?

• A. $105$
• B. $217$
• C. $7$
• D. $31$

Answer 1

The correct option is A $105$

Now if some or all of n things be taken at a time, then the number of combinations will be $2^n$ - 1, as explained below. Each of the things can be taken or left, i.e. each gives 2 combinations. So the combinations of n things will be $2^n$.But this includes the case when all have been left. Hence the number of combinations will he $2^n$ - 1

Section A : 3 questions, Section B: 4 questions; and one question from each section is compulsory i.e. all of a particular section cannot be left.

$\therefore$ $2^3$ - 1 = 7, $2^4$ -1 = 15

$\therefore$ Total is 7 x 15 = 105 by fundamental theorem.