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# If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (ii) the repetition of digits is not allowed?

9.(ii) If -digit numbers greater than    are randomly formed from the digits  and , what is the probability of forming a number divisible by when, (ii) the repetition of digits is not allowed?

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(ii)

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 not allowed,

The remaining 3 places can be filled by remaining 4 digits in   ways.

Total number of 4-digit numbers greater than 5000 =

We know, a number is divisible by 5 if unit’s place digit is either 0 or 5.

Case 1. When digit at  place is 5, the units place can be filled only with 0.

And the  &  places can be filled with any two of the remaining digits {1,3,7} in

Number of 4-digit numbers starting with 5 and divisible by 5 =

Case 2. When digit at  place is 7, the units place can be filled by 0 or 5 in 2 ways.

And the  &  places can be filled with any two of the remaining 3 digits in

Number of 4-digit numbers starting with 7 and divisible by 5 =

Total number of 4-digit numbers greater than 5000 that are divisible by 5 = 6 + 12 = 18

Therefore, the required probability =

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