There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a…

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
  1. 750
  2. 1500
  3. 2255
  4. 2250

Solution

Total number of ways $\begin{aligned} &={ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_3+{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_2 \\ &+{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_3 \times{ }^5 \mathrm{C}_1+{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_2 \\ &+{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_2 \times{ }^5 \mathrm{C}_1+{ }^5 \mathrm{C}_3 \times{ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_1 \\ &=5 \times 5 \times 10+5 \times 10 \times 10+5 \times 10 \times 5 \\ & \quad+10 \times 5 \times 10+10 \times 10 \times 5+10 \times 5 \times 5 \\ &= 250+500+250+500+500+250 \\ &= 2250 \end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 2)

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