Solve the problem.
-An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 5 of the multiple-choice questions and 2 of the essay questions, in how many ways can the questions be chosen?
A)1890
B)453,600
C)261,273,600
D)540

Question

Quizplus · Accepted Answer

The number of ways to choose 5 out of 9 multiple-choice questions is $C(9,5) = \frac{9!}{5!(9-5)!} = 126$, and the number of ways to choose 2 out of 6 essay questions is $C(6,2) = \frac{6!}{2!(6-2)!} = 15$. The total number of ways to choose the questions is the product of these two, which is $126 \times 15 = 1890$.

Solve the Problem. -An Exam Consists of 9 Multiple-Choice Questions and 6 Essay