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Probability

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156
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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

#1
+2541
+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
+2541
+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 $${24 + 6 \over 120} = \color{brown}\boxed{1 \over 4}$$

BuilderBoi Apr 17, 2022
#2
+124696
+1

Very nice, BuilderBoi   !!!!

CPhill  Apr 18, 2022