Exam!

Probability Level 4

There are 12 questions in an exam and each student must answer 8 questions including at least 4 of the first five questions.

How many different combinations of questions can a student choose to answer?

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The answer is 210.

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User 123
Jan 9, 2015

CASE 1: THE STUDENT CHOOSES $4$ OUT OF THE FIRST $5$ QUESTIONS

The number of combinations of $4$ questions chosen out of the first $5$ questions is $5C4 = 5$

The number of combinations of $4$ questions chosen out of the remaining $7$ questions is $7C4 = 35$

The total number of combinations of questions is $5\times 35 = 175$

CASE 2: THE STUDENT CHOOSES THE FIRST $5$ QUESTIONS

The number of combinations of $5$ questions chosen out of the first $5$ questions is $5C5 = 1$

The number of combinations of $3$ questions chosen out of the remaining $7$ questions is $7C3 = 35$

The total number of combinations of questions is $1\times 35 = 35$

Adding CASE 1 and CASE 2, there are $175 + 35 = 210$ combinations of choosing question.

Satyen Nabar
Jan 9, 2015

1) If you choose to answer 12345 -- you can choose to answer remaining 3 questions in 7C3 ways = 35 ways.

2) If you choose to answer 4 out of first 5 you can select them in 5C4 = 5 ways. Remaining 4 questions can be chosen in 7C4 ways = 35. So 35 *5 = 175 ways

Total = 175 +35 = 210 ways.

i didnt tink tat the person wud attend 1,2,3,4,5 ...... i jus split like 7C4 * 5C4 ...... super approach to problem sir !!

Ganesh Ayyappan - 6 years, 5 months ago

actually the problem states that the student must answer at least 4 of the first 5 questions, so the case where the student attempts to answer the first 5 questions is valid and is to be considered

Yvanne Paolo Yutuc - 6 years, 4 months ago

Exam!

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The answer is 210.

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