We’re using 5
5
digits to form the number, so the result is always going to be a five digit number. Notice, for it to be greater than 40000
40000
, the ten-thousands digit must be greater than or equal to 4
4
. After that, the units digit must be even. Since 4
4
and 6
6
are both even and can also be the ten-thousands digit, we make special cases for those. Let’s start with 5
5
We’d have 3
3
choices for the units digit (2,4,6), and then the other 3 digits can be arranged in any way, giving 3⋅3!=18
3
⋅
3
!
=
18
numbers.
If we have 4
4
or 6
6
as the ten-thousands digit, there’d be 2
2
choices for the units digit (2, and the other), and the rest can be arranged in any way, giving 2⋅3!=12
2
⋅
3
!
=
12
.
So there’s a total of 18+12+12=42
18
+
12
+
12
=
42
numbers.
