How many three digit numbers have the sum of their digits as 23?

Puzzling

C(25,2) - C(3,1) * C(15,2) + C(3,2) * C(5,2) = 15

Anonymous

1 599 2 689 3 698 4 779 5 788 6 797 7 869 8 878 9 887 10 896 11 959 12 968 13 977 14 986 15 995

Krishnamurthy

599, 689, 698, 779, 788, 797, 869, 878, 887, 896, 959, 968, 977, 986, and 995 ----> Total: 15