There are 3 sections in a question paper and each

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:

  1. (1) 3000

  2. (2) 1500

  3. (3) 2255

  4. (4) 2250


Correct Option: , 4

Solution:

(4) Since, each section has 5 questions.

$\therefore$ Total number of selection of 5 questions

$=3 \times{ }^{5} C_{1} \times{ }^{5} C_{1} \times{ }^{5} C_{3}+3 \times{ }^{5} C_{1} \times{ }^{5} C_{2} \times{ }^{5} C_{2}$

$=3 \times 5 \times 5 \times 10+3 \times 5 \times 10 \times 10$

$=750+1500=2250$

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