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 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?
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For problems with multiple sections and compulsory choices, compute the number of ways for each section and multiply using the counting principle.
Updated On: Jul 18, 2026
- 105
- 210
- \(2^7\)
- \(2^5\)
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The Correct Option is A
Solution and Explanation
Step 1: Section 1 selection.
Section 1 has 3 questions. Candidate must choose at least 1 question: \[ \binom{3}{1} + \binom{3}{2} + \binom{3}{3} = 3 + 3 + 1 = 7 \]
Step 2: Section 2 selection.
Section 2 has 4 questions. Candidate must choose at least 1 question: \[ \binom{4}{1} + \binom{4}{2} + \binom{4}{3} + \binom{4}{4} = 4 + 6 + 4 + 1 = 15 \]
Step 3: Total selections.
\[ \text{Total ways} = 7 \cdot 15 = 105 \]
Step 4: Final conclusion.
\[ \boxed{105} \]
Section 1 has 3 questions. Candidate must choose at least 1 question: \[ \binom{3}{1} + \binom{3}{2} + \binom{3}{3} = 3 + 3 + 1 = 7 \]
Step 2: Section 2 selection.
Section 2 has 4 questions. Candidate must choose at least 1 question: \[ \binom{4}{1} + \binom{4}{2} + \binom{4}{3} + \binom{4}{4} = 4 + 6 + 4 + 1 = 15 \]
Step 3: Total selections.
\[ \text{Total ways} = 7 \cdot 15 = 105 \]
Step 4: Final conclusion.
\[ \boxed{105} \]
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