‌ Any possible sum of ‌(1,2,3,...,8)(=a‌ say ‌)
36
∵‌
a
36
≥‌
4
5
∴a≥29 If one of the number from {1,2,......,8} is left then total a≥29 by 3 ways. Similarly by leaving terms more 2 or 3 we get 16 more combinations. ∴ Total number of different set A possible is 16+3=19