1. ## combination

"A question paper is divided into two groups, each containing 5 questions. A candidate is required to solve 6 questions in all but he is not permitted to attempt more than 4 questions from each group. Find the number of ways in which the candidate can select the question."

I thought he could either choose 3 from each group, or choose 4 from one group and 2 from the other. (5C3)(5C3)+(5C4)(5C2)=150 but the answer is supposed to be 200. I thought of multiplying 150 by 2 because choosing three from group 1 and three from group 2 is distinct from doing it the other way around. But that's 300, and the answer is supposed to be 200. Please assist.

2. Originally Posted by Pewł
"A question paper is divided into two groups, each containing 5 questions. A candidate is required to solve 6 questions in all but he is not permitted to attempt more than 4 questions from each group. Find the number of ways in which the candidate can select the question."

I thought he could either choose 3 from each group, or choose 4 from one group and 2 from the other. (5C3)(5C3)+(5C4)(5C2)=150 but the answer is supposed to be 200. I thought of multiplying 150 by 2 because choosing three from group 1 and three from group 2 is distinct from doing it the other way around. But that's 300, and the answer is supposed to be 200. Please assist.
The number of choices is $\displaystyle {5\choose 4}{5\choose2}+{5\choose 3}{5\choose 3}+{5\choose 2}{5\choose 4}=200$ since you can choose:

4 Q's from Group 1 and 2 Q's from Group 2 OR
3 Q's from Group 1 and 3 Q's from Group 2 OR
2 Q's from Group 1 and 4 Q's from Group 2