How many natural numbers less than $10^8$ are there, whose sum of digits equals $7$?

Question

How many natural numbers less than $10^8$ are there, whose sum of digits equals $7$?

I got it here.But is there any more effecient and easier way to solve than the link shows?

Answer 1

The numbers have 8 places (some of which might be zero), and there are 7 units of value to go into them. (Each place can have at most 9 units, but that's automatic since there's only 7 units total.) So it's a stars and bars problem with 7 stars and 7 bars, making $\binom{14}{7} = 3432$ such numbers.

(For example, |**|*|***|||*| would correspond to the number 02130010.)

[edited: 8 places, not 7]

Answer 2

C++ program for your problem:

#include < iostream>

using namespace std;

int main() {

int count=0;

int sum(int x);

for (int i=1;i<100000000;i++){

if (sum(i)==7)

count++;

}

cout < < count< < endl;

return 0;

}

int sum (int x){

int add=0;

while(x){

add=add+x%10;
x=x/10;
}

return add; }