The number of positive integers greater than 6000 but not more than 7000, divisible by 5, using the digits 0,1,2,........9, if any digit can be used any numbers of times, is

200

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112

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119

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None of these

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Solution

The correct option is A
200

A number is divisible by 5 if it ends with 5 or 0. Numbers ending with 0. First place must be filled by 6. Second and third places can be filled in again 10 ways. $∴$ There are 100 numbers ending with 0. Similarly there are 100 numbers ending with 5. Therefore, total number of numbers =200
Note: Excusion of 6000 and inclusion of 7000 does not effect the counting.

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