### Instruction: 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 500,000? Express your answer as a common fraction.### Response: To form a six-digit multiple of 5, the last digit must be either 0 or 5.
Since there is no 0 in the digits from 1 to 6, the last digit must be 5.
That means the first digit must be either 1, 2, 3, 4, or 6, since I cannot repeat 5.
To make the number greater than 500,000, the first digit must be either 5 or 6.
But 5 is already used as the last digit, so the first digit must be 6.
That leaves me with four digits to arrange in the middle: 1, 2, 3, and 4.
There are 4! = 24 ways to arrange these four digits.
Therefore, the total number of six-digit multiples of 5 that are greater than 500,000 is 24.
The total number of six-digit multiples of 5 that can be formed from the digits 1 to 6 is 5 x 4! = 120, since there are 5 choices for the first digit and 4! ways to arrange the remaining four digits.
The probability of forming a six-digit multiple of 5 that is greater than 500,000 is the ratio of the favorable outcomes to the total outcomes.
This ratio is 24/120, which simplifies to 1/5.