I have been given the problem to solve how many even integers with no repeated digits between 20,000 and 70,000.

my first thought was to have the set X = {0,1,2,3,4,5,6,7,8,9}

and then propose there are 5 positions in which these numbers can be placed, being ABCDE

therefore E has to be either {0,2,4,6,8} => |E| = 5

D is any other of the 10 ten numbers excluding E => |D| = 8 and so on.

therefore i originally thought that the answer would be 5x9x8x7x2 (using the mulitplication prinicple)

As A is either 2,3,4,5,6,7 and cant be what B,C,D was therefore |A| = 2, i know that this is not true as BCD can be numbers outside of this region. but i am unclear as to how to find |A| without knowing what values B,C,D took on? any help would be appreciated.

Thanks

Reece