MHB Test question combination question

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To solve the exam question combination problem, students must answer 8 questions, including at least 4 from the first 5. The combinations can be calculated in two scenarios: choosing 4 from the first 5 and 4 from the remaining 7, or choosing 5 from the first 5 and 3 from the remaining 7. The number of ways to select 4 from the first 5 is 6, calculated as 5C4 + 5C5. By adding the combinations from both scenarios, the total number of different question combinations can be determined.
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There are 12 questions on an exam, and each student must answer 8 questions including at least 4 of the first 5 questions. How many different combinations of questions could a student choose to answer?

So I got the number of ways a student can choose to answer the first 5 questions which is 6 (5C4 + 5C5). I'm not sure what else to do.
 
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Raerin said:
There are 12 questions on an exam, and each student must answer 8 questions including at least 4 of the first 5 questions. How many different combinations of questions could a student choose to answer?

So I got the number of ways a student can choose to answer the first 5 questions which is 6 (5C4 + 5C5). I'm not sure what else to do.

The total number answered must be 8 and there are two ways of doing this with the other constraint.

1: 4 from the first 5 questions, 4 from the last 7
2: 5 from the first 5 questions, 3 from the last 7

Add up (1) and (2) and you'll get the answer.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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