Question: A candidate is required to answer 6 out of 10 questions divided into 2 groups each containing 5 questions. He can attempt maximum 4 questions from each group. In how many ways can he make up his choice ?

(A) 660
(B) 566
(C) 260
(D) 200
(E) 100

Correct Answer: D
Solution and Explanation:
Approach Solution 1:
So two sets of 5 questions each. We are looking at ways to select these 6 questions.

Thus, a combination question.

Two ways
1) 5C4*5C2=5*10=50.
Vice versa too is possible, so another 50.
2) 5C3*5C3=10*10=100

Total: 50+50+100= 200

Approach Solution 2:
We can split the two groups into group A and group B, thus the groups are independent.

We need to answer 6 questions while picking more than 4 from any group, so we can do 4 + 2, 3 + 3, or 2 + 4. This corresponds to :

5C4∗5C2+5C3∗5C3+5C2∗5C4=5∗10+10∗10+10∗5= 200

Approach Solution 3:
Solution:

The question can be answered in one of the following cases:

1) 4 questions from group one and 2 questions from group two
2) 3 questions from group one and 3 questions from group two
3) 2 questions from group one and 4 questions from group two

The two groups have the same number of questions. Therefore, the number of ways to answer the questions in case 3 is the same as in case 1. Now, let’s determine the number of ways to answer the questions in the first two cases:

Case 1: 4 questions from group one and 2 questions from group two

5C4 x 5C2 = 5 x 10 = 50

Case 2: 3 questions from group one and 3 questions from group two

5C3 x 5C3 = 10 x 10 = 100

Case 3:
(gives the same result as Case 1), or 50

Therefore, the answer to the questions in 50 + 100 + 50 = 200 ways.

“A candidate is required to answer 6 out of 10 questions divided into 2”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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