A physics exam consists of 9 multiple choice questions and 6 open-ended problems in which all work must be shown.If an examinee must answer 6 of the multiple- choice questions and 3 of the open-ended problems, in how many ways can the questions and problems be chosen?
87
To find the number of ways to choose the questions and problems, you can use the concept of combinations.
For the multiple-choice questions, you need to choose 6 out of 9 questions. This can be calculated using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen.
In this case, the number of ways to choose 6 multiple-choice questions can be calculated as C(9, 6) = 9! / (6!(9-6)!) = 9! / (6!3!) = (9 * 8 * 7) / (3 * 2 * 1) = 84.
For the open-ended problems, you need to choose 3 out of 6 problems. Using the same combination formula, you can calculate the number of ways to choose them as C(6, 3) = 6! / (3!(6-3)!) = 6! / (3!3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20.
Finally, to find the total number of ways to choose both the questions and problems, you can multiply the number of ways to choose each individually: 84 * 20 = 1680.
Therefore, there are 1680 ways to choose the 6 multiple-choice questions and 3 open-ended problems for the physics exam.