Question

In how many ways can a four digit even number with distinct digits be formed

Answer 1

My attempt to solve this problem is:

First digit cannot be zero, so the number of choices only 6(1,2,3,4,5,6)6(1,2,3,4,5,6)

The last digit can be pick from 0,2,4,60,2,4,6, so the number of choices only 4

Second digit can be only pick from the rest, so the number of choices only 5

Third digit can be only pick from the rest, so the number of choices only 4

The total number of choices is 6⋅4⋅5⋅4=4806⋅4⋅5⋅4=480

So, is my solution true? Or I miss something? Thanks