Kenneth Rosen Ex 5.5 closed

Question

How many positive integers less than 1,000,000 have the sum of their digits equal to 19?

Comments

I am little doubtful with regard to below points.

The equation I understood is

d1 +d2 + d3+ d4+d5+d6=19

where each  0$\leq$d_i$\leq$9 (Actually answer comes when  I take each d_i in this range)

my query was why not each d_i will be in range 1$\leq$d_i$\leq$9

because question mentions for positive integers so each digit must be from 1 to 9.

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yes,that will be equation

ans 42504?

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@Ayush it's because 1 digit number can be written as 00000 or 000001 or 0000002 or so on..

I mean, 000 289 = 19 is also a possibility.

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https://gateoverflow.in/85604/generalized-permutation-and-combination

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@Srestha-No it's 30492.

I think Why di ranges from 0 to 9 because

Firstly the question says

"the sum of digits must be 19"

so with all zeroes, I cannot have sum as 19 (so obviously there would be a positive integer whose sum of digit would be 19)

and since with up to 6 digits, each digit can range from 0 to 9 only that's why each di is from 0 to 9.