How many positive integers less than 1,000,000 have the
sum of their digits equal to 19?
Doubt 1: I understood till C(24,5). Now while subtracting unfavorable cases, for the sum not to exceed 19 one or more digits cannot exceed 9 coz 10+10= >19. But each digit can only have values from 0-9. how could a digit take a value 10?
My approach : It is similar to selection with repetition allowed. We have to select 19 balls from 6 boxes. Now to violate the condition, not more than 9 balls should be removed from more than one box, otherwise it will be 20. So suppose I take out 10 balls from box 1, still 9 more balls are remaining. It is same as selecting 9 balls from 6 boxes with repetition allowed. Then how it is unfavorable according to solution given?
plz correct me.
