# GMAT 700+ Quant Practice Question 22

#### Counting Methods | Permutation Combination Practice

The given question is a challenging GMAT 700+ level quant problem solving question testing concepts in permutation combination (counting methods). A very interesting practice question to understand how to list down possibilities and then count outcomes for each of those possibilities.

Question 22: A student is required to solve 6 out of the 10 questions in a test. The questions are divided into two sections of 5 questions each. In how many ways can the student select the questions to solve if not more than 4 questions can be chosen from either section?

1. 100
2. 210
3. 150
4. 200
5. 105

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### Explanatory Answer | GMAT Permutation Combination Practice Question

#### Step 1: List Down Possibilities

The student is required to solve 6 out of 10 questions.
Questions are divided into 2 sections of 5 questions each.
Not more than 4 questions can be selected from any section.

#### Step 2: List Down Possibilities

Section Possibility 1 Possibility 2 Possibility 3
Section 1 4 3 2
Section 2 2 3 4

#### Step 3: Count Number of Outcomes for each Possibility and Add

Possibility 1: Section 1: 4 Questions | Section 2: 2 Questions
This can be done in 5C4 × 5C2 = 5 × 10 = 50 ways

Possibility 2: Section 2: 3 Questions | Section 2: 3 Questions
This can be done in 5C3 × 5C3 = 10 × 10 = 100 ways

Possibility 3: Section 1: 2 Questions | Section 2: 4 Questions
This can be done in 5C2 × 5C4 = 10 × 5 = 50 ways

Total number of ways = 50 + 100 + 50 = 200 ways

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