Find the number of positive integers greater than 6000 and less than 7

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.

Answer»

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	TO	O
1	8	7	2

So, the total number of integers = 1 × 8 × 7 × 2 = 112

Hence, the required number of integers = 112