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The digits from 1 to 6 are arranged to form a six-digit multiple of 5. What is the probability that the number is greater than \(450,000\)? Express your answer as a common fraction.

 Apr 17, 2022

Best Answer 

 #1
avatar+1384 
+1

Because the number must be a multiple of 5, the final digit must be a 5. 

 

There are \(5! = 120\) ways to order the other digits. 

 

For the number to \(>450,000\), the numbers can be in the order \(46\text{_,__}5\) or \(6 \text{__,__5}\)

 

For the first case, there are \(3! = 6\) ways to order the 3 remaining digits. 

 

For the second case, there are \(4! = 24\) ways to order the remaining 4 digits. 

 

Thus, the probability is \({24 + 6 \over 120} = \color{brown}\boxed{1 \over 4}\)

 Apr 17, 2022
 #1
avatar+1384 
+1
Best Answer

Because the number must be a multiple of 5, the final digit must be a 5. 

 

There are \(5! = 120\) ways to order the other digits. 

 

For the number to \(>450,000\), the numbers can be in the order \(46\text{_,__}5\) or \(6 \text{__,__5}\)

 

For the first case, there are \(3! = 6\) ways to order the 3 remaining digits. 

 

For the second case, there are \(4! = 24\) ways to order the remaining 4 digits. 

 

Thus, the probability is \({24 + 6 \over 120} = \color{brown}\boxed{1 \over 4}\)

BuilderBoi Apr 17, 2022
 #2
avatar+122390 
+1

Very nice, BuilderBoi   !!!!

 

 

cool cool cool

CPhill  Apr 18, 2022

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