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?

- 100
- 210
- 150
- 200
- 105

@ INR

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.

Section | Possibility 1 | Possibility 2 | Possibility 3 |
---|---|---|---|

Section 1 | 4 | 3 | 2 |

Section 2 | 2 | 3 | 4 |

**Possibility 1**: Section 1: 4 Questions | Section 2: 2 Questions

This can be done in 5C_{4} × 5C_{2} = 5 × 10 = 50 ways

**Possibility 2**: Section 2: 3 Questions | Section 2: 3 Questions

This can be done in 5C_{3} × 5C_{3} = 10 × 10 = 100 ways

**Possibility 3**: Section 1: 2 Questions | Section 2: 4 Questions

This can be done in 5C_{2} × 5C_{4} = 10 × 5 = 50 ways

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

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