Final answer:
The total number of ways a candidate can answer 6 multiple-choice questions with exactly 4 correct answers is calculated by first choosing the 4 questions to answer correctly and then choosing incorrect answers for the remaining questions. The calculation C(6,4) × 3^2 = 135, though this option is not provided in the multiple-choice answers provided with the question.
Step-by-step explanation:
The question involves calculating the number of ways a candidate can answer a test with multiple-choice questions, specifically when a certain number of answers are correct. The test consists of 6 questions each with 4 possible answers, and we want to find out the number of ways to get exactly 4 correct answers.
First, we choose which 4 questions out of the 6 are answered correctly. This can be done in C(6,4) ways (which is the combination of 6 things taken 4 at a time). Then, for the remaining 2 questions, we need to choose incorrect answers. Since there are 3 incorrect answers for each question, this can be done in 32 ways.
Therefore, the total number of ways is the product of these two numbers of outcomes: C(6,4) × 32. Calculating this, we have C(6,4) = 15 and 32 = 9. Multiplying these together gives 15 × 9 = 135. However, since 135 is not one of the provided options in the multiple-choice answers, there seems to be a mistake either in the question or provided options. If this is a typo in the options and 135 was meant to be included, that would be the correct number of ways.