Find number of four-digit numbers in which repetition is not allowed.

Explanation

Since number is even, unit place can be filled with 0, 2, 4, 6 or 8. Also thousand's place cannot be filled with '0'.
Now number of digits available for thousand's place depend upon whether '0' is used or not at unit place.
So, here we will be having two cases.
Case I : Zero at unit place
In this case for thousand's place all nine non-zero digits are available.
The options for different places are as shown in the following figure.

So, number of numbers `=9xx8xx7=504`
Case II : Zero is not at unit place.

In this case for unit place we have four options (2,4,6 or 8)
For thousand's place, we have 8 non-zero digits available.
For hundred's place, we have again 8 digits available as digits used in thousand's place and unit place cannot be used, but digit '0' can be used.
Subsequently for ten's place we have 7 options.
So, number of numbers `=8xx8xx7xx4=1792`
Therefore, total number of numbers `=504+1792=2296`