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Question
Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
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Solution
Any number divisible by 5, its unit place must have 0 or 5 We have to find 4-digit number greater than 6000 and less than 7000.
So, the unit place can be filled with 2 ways (0 or 5) since, repetition is not allowed
∴ Tens place can be filled with 7 ways and hundreds place can be filled with 8 ways.
But the required number is greater than 6000 and less than 7000.
So, thousand place can be filled with 1 digits i.e. 6
Th H T O
1 8 7 2
So, the total number of integers = 1 × 8 × 7 × 2 = 112
Hence, the required number of integers = 112
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