Question

How many 4-digit numbers less than 7000 can be formed using digits 0, 5, 7, 1, 2, 6, and 8 without repetition?

Answer 1

Finding the number of 4-digit numbers less than 7000 that can be formed using digits 0, 5, 7, 1, 2, 6, and 8 (used only once) is similar to filling 4 vacant places with 7 different things with some constraints.


Constraint: For numbers less than 7000, the digit in the thousands place cannot be 7, 0, or 8.

So, there are 4 possibilities of filling the thousands place.

For remaining places, there are no constraints.

So, hundreds, tens, and units places can be filled in 6, 5, and 4 ways, respectively.

∴ Total number of 4-digit numbers less than 7000 that are formed are $4\times 6\times 5\times 4=480$