A state Motor Vehicle Department requires learners to pass a written test on the motor vehicle laws of the state. The exam consists of fourteen true-or-false questions, of which twelve must be answered correctly to qualify for a permit. In how many different ways can a learner who answers all the questions on the exam qualify for a permit?
A) 106
B) 113
C) 104
D) 112
E) 105

Question

A state Motor Vehicle Department requires learners to pass a written test on the motor vehicle laws of the state. The exam consists of fourteen true-or-false questions, of which twelve must be answered correctly to qualify for a permit. In how many different ways can a learner who answers all the questions on the exam qualify for a permit? ​
A) 106
B) 113
C) 104
D) 112
E) 105

Quizplus · Accepted Answer

To qualify, a learner must answer at least 12 out of 14 questions correctly. The number of ways to choose 12, 13, or 14 correct answers from 14 questions is calculated using combinations: C(14,12) + C(14,13) + C(14,14) = 91 + 14 + 1 = 106.

A State Motor Vehicle Department Requires Learners to Pass a Written