Question

There are $3$ sections in a question paper and each section contains $5$ questions. A candidate has to answer a total of $5$ questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:

• A. $2250$
• B. $2255$
• C. $1500$
• D. $3000$

Answer 1

The correct option is A $2250$

There are $6$ possible cases.
$\begin{array}{ccc}S-1& S-2& S-3\\ 1,2,3,4,5& 1,2,3,4,5& 1,2,3,4,5\\ 1& 1& 3\\ 1& 2& 2\\ 1& 3& 1\\ 2& 2& 1\\ 2& 1& 2\\ 3& 1& 1\end{array}$

Total number of selection
$=3{(}^5{\text{C}}_1\times {}^5{\text{C}}_2\times {}^5{\text{C}}_2)+3{(}^5{\text{C}}_1\times {}^5{\text{C}}_1\times {}^5{\text{C}}_3)$
$=3(5\times 5\times 2\times 5\times 2)+3(5\times 5\times 10)$
$=1500+750=2250$