Question

how many 4 digit even numbers are there with all 4 digit distinct?

Answer 1

For a number to be even it should end with zero or even numbers i.e., 0, 2, 4, 6, 8

Now, number of four digit even number with all digit distinct having 0 at its unit place = 9 × 8 × 7 × 1 = 504

and number of four digit even number with all digit distinct having 2 or 4 or 6 or 8 at its unit place = 8 × 8 × 7 × 4 = 1792
(since zero cannot be fixed in thousand's place)
Hence, required total 4 digit even number with all digit distinct = 504 + 1792 = 2296