Q59 / 150 · MHT CET 2024 (15 May Shift 2) · Mathematics
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
- A750
- B1500
- C2255
- Correct answerD2250
Solution
Total number of ways
$\begin{aligned}
&={ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_3+{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_2 \\
&+{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_3 \times{ }^5 \mathrm{C}_1+{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_2 \\
&+{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_1+{ }^5 \mathrm{C}_3 \times{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_1 \\
&=5 \times 5 \times 10+5 \times 10 \times 10+5 \times 10 \times 5 \\
& \quad+10 \times 5 \times 10+10 \times 10 \times 5+10 \times 5 \times 5 \\
&= 250+500+250+500+500+250 \\
&= 2250
\end{aligned}$
Hence, the correct answer is option: 'D'.