Solve Counting Problems Using Combinations
-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
A) 1680
B) 972
C) 261,273,600
D) 7,257,600

Question

Quizplus · Accepted Answer

The number of ways to choose 6 multiple-choice questions from 9 is C(9,6) = 84. The number of ways to choose 3 open-ended problems from 6 is C(6,3) = 20. The total number of ways is 84 * 20 = 1680.