Question

A question paper consists of two sections having respectively $3$ and $5$ questions. The following note is given on the paper$‘‘\text{It is not necessary to attempt all the questions. One question from each section is compulsory"}$. In how many ways can a candidate select the questions?

• A. 216
• B. 217
• C. 224
• D. 225

Answer 1

The correct option is B 217

Here we have $2$ sections (say) $A$ and $B$. The section $A$ has $3$ questions and section $B$ has $5$ questions. One question
from each section is compulsory according to the given condition.
$\therefore$ Number of ways of selecting one or more than one question from section $A$ is $2^3-1=7.$
And number of ways selecting one or more than one questions from section $B$ is $2^5-1=31.$
Hence by the principle of multiplication, the required number of ways in
which a candidate can select the questions $=7\times 31=217$.