Answer:
There are 18 ways to fill out the answer sheet so that eight answers are correct and one is incorrect.
Explanation:
Consider the provided information.
A multiple choice test consists of nine questions, each of which has three choices.
We need to find the number of ways so that eight answers are correct and one is incorrect.
There is only one correct answer and for incorrect answer we have only 2 choices because 1 choice is correct.
Thus the number of possible ways are:
(2×1×1×1×1×1×1×1×1)+(1×2×1×1×1×1×1×1×1)+(1×1×2×1×1×1×1×1×1)+(1×1×1×2×1×1×1×1×1)+(1×1×1×1×2×1×1×1×1)+(1×1×1×1×1×2×1×1×1)+(1×1×1×1×1×1×2×1×1)+(1×1×1×1×1×1×1×2×1)+(1×1×1×1×1×1×1×1×2) = 2+2+2+2+2+2+2+2+2 = 18
There are 18 ways to fill out the answer sheet so that eight answers are correct and one is incorrect.