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.
 

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