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[SOLVED] Test question combination question

Raerin

Member
Oct 7, 2013
46
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.
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,052
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.