How many numbers less than 1000 have all their digits even or zero and and sum of their digits as 10?

In this question possibilities are very few and therefore we can manually enumerate those-
They are only four combinations-
0,2,8 i.e can be arranged in 3! ways
2,2,6 i.e in 3!/2! ways
0,4,6 i.e in 3! ways
2,4,4 i.e in 3!/2! ways
Adding all the combinations, we will get the answer as 18
ANS: 18