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.
+2668 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 \({24 + 6 \over 120} = \color{brown}\boxed{1 \over 4}\)
+2668 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 \({24 + 6 \over 120} = \color{brown}\boxed{1 \over 4}\)
