In an examination, a student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can these questions be chosen?

There are total 13 questions out of which 10 is to be answered .The student can answer in the following ways:


6 questions from part A and 4 from part B


5 questions from part A and 5 from part B


4 questions from part A and 6 from part B


⇒total ways in the 1st case are 6C67C4


⇒ total ways in the 2nd case are 6C57C5


⇒ total ways in the 3rd case are 6C47C6


= 6C67C4+6C57C56C47C6


Applying nCr =


= 266 ways.


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