9.(i) If -digit numbers greater than are randomly formed from the digits and , what is the probability of forming a number divisible by when, (i) the digits are repeated?
Since 4-digit numbers greater than 5000 are to be formed,
The place digit can be filled up by either 7 or 5 in ways
Since repetition is allowed,
Each of the remaining 3 places can be filled by any of the digits 0, 1, 3, 5, or 7 in ways.
Total number of 4-digit numbers greater than 5000 =
(5000 cannot be counted, hence one less)
We know, a number is divisible by 5 if unit’s place digit is either 0 or 5.
Total number of 4-digit numbers greater than 5000 that are divisible by 5 =
Therefore, the required probability =
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