Question

(1, 1, 8) is a triple of natural numbers which has a sum of 10. Consider (1, 8, 1) and (8, 1, 1) to be the same triple as (1, 1, 8). How many different triples of natural numbers have a sum of 10? Include (1, 1, 8) as one of your triples.

Answer 1

since order does not matter, start small and work your way up.
1,1,8
1,2,7
1,3,6
...
3,3,4

Answer 2

Is there any quicker way?

Answer 3

No there is not a quicker way unless you want to use a computer code to cheat/get a hint.