Question

Consider all positive integers with 7 digits (first digit not being zero.) How many of them are even and have all seven digits distinct?

Answer 1

BLAH BLAH

Answer 2

\[9\times 9\times 8\times 7\times 6\times 5\times 4\]

Answer 3

left most digit can't be a zero, and then the next one can't be the one chosen previously, etc

Answer 4

9*9*8*7*6*5*4 = 544,320 which is incorrect.

The hint I get is to consider all cases in which the digit is not zero. I am confused.