# combination

• Aug 21st 2009, 10:49 PM
Pewł
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.
• Aug 22nd 2009, 12:45 AM
Chris L T521
Quote:

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 ${5\choose 4}{5\choose2}+{5\choose 3}{5\choose 3}+{5\choose 2}{5\choose 4}=200$ 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