Question

A question paper consists of two sections having 3 and 4 questions respectively. One question from each section is compulsory. In how many ways can a candidate select the questions?

• A. 105
• B. 210
• C. \(2^7\)
• D. \(2^5\)

Hint:

For problems with multiple sections and compulsory choices, compute the number of ways for each section and multiply using the counting principle.

Answer 1

The Correct Option is A

Step 1: Use the at-least-one-chosen counting shortcut for each section.
For a section with \(n\) questions where at least one must be picked, the number of ways is \(2^n-1\), that is every subset except the empty one.

Step 2: Apply it to both sections.
Section 1 has 3 questions: \(2^3-1=7\) ways.
Section 2 has 4 questions: \(2^4-1=15\) ways.

Step 3: Multiply since the two choices are independent.
\[ 7\times15=105 \]

Step 4: Conclusion.
\[ \boxed{105} \]