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?

Guest Apr 15, 2022

#1**+1 **

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.

BuilderBoi Apr 15, 2022

#1**+1 **

Best Answer

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.

BuilderBoi Apr 15, 2022

#2**+2 **

You are very good at this counting stuff......I'm usually stuck on many of these !!!

CPhill
Apr 15, 2022

#3**+5 **

That is true,

You seem to get these counting and prob questions with ease. These type of questions always mess up my brain!!!

**-Vinculum**

Vinculum
Apr 15, 2022

#4**0 **

Thank You!!! I grinded AoPS Counting and Probability for a month, and I guess it's paying off now...

BuilderBoi
Apr 15, 2022