Question

3. An exam Question paper contains 4 sections, each section contains 6 questions. In how many ways can a person answer 17 questions so that he answers at least 4 questions
from each section
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Answer 1

Given:

Total number of sections in question paper = 4

Number of questions in each section = 6

Number of questions to be attempted = 17

To find:

We have to find in how many ways a total of 17 questions to be answered with  at least 4 questions from each section

Solution:

As we have to choose compulsorily 4 questions from each section that can be done in ⁶C₄×4 ways

So a total of 16 questions have been chosen now

For the left 1 question we can choose in ²C₁×4 ways

So total ways= ⁶C₄×4ײC₁×4

                      = 16 × 15 × 2

                      = 480

∴ A person can answer 17 questions with at least 4 questions from each section  in  480 ways