How many ways are there to answer a 10-question true/false test, where at least \(8\) of the questions have been answered with a false?
+2668 There are 2 options for 1 question
There are another 2 options for the other question
The remaining 8 must all be false.
There are \(10 \choose 8 \) ways to choose which questions are guaranteed to be false
So, in total, there is: \(2 \times 2 \times {10 \choose 8} = \color{brown}\boxed{180}\) ways to answer.
+2668 There are 2 options for 1 question
There are another 2 options for the other question
The remaining 8 must all be false.
There are \(10 \choose 8 \) ways to choose which questions are guaranteed to be false
So, in total, there is: \(2 \times 2 \times {10 \choose 8} = \color{brown}\boxed{180}\) ways to answer.
+130552 You are very good at this counting stuff......I'm usually stuck on many of these !!!
+580 That is true,
You seem to get these counting and prob questions with ease. These type of questions always mess up my brain!!!
-Vinculum
+2668 Thank You!!! I grinded AoPS Counting and Probability for a month, and I guess it's paying off now...
