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?
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?

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 6C6 X7C4

⇒ total ways in the 2nd case are 6C5 X7C5

⇒ total ways in the 3rd case are 6C4 X7C6

= 6C6 X 7C4

6C5 X7C5 +6C4 X7C6

Applying nCr

= 266 ways.