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?

Question

Philoid · Accepted Answer

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 ⁿC_r =

= 266 ways.