+0  
 
0
105
4
avatar

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?

 Apr 15, 2022

Best Answer 

 #1
avatar+2455 
+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. 

 Apr 15, 2022
 #1
avatar+2455 
+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
avatar+124598 
+2

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

 

 

cool cool cool

CPhill  Apr 15, 2022
 #3
avatar+578 
+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

 

smileysmileysmiley

Vinculum  Apr 15, 2022
 #4
avatar+2455 
0

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

BuilderBoi  Apr 15, 2022

33 Online Users