**How many natural numbers less that are there, whose sum of digits equals 7?**

**Solution:**

Consider the equation

Number of non negative integer solutions to this equation is

The set of solutions is bijective with the number of numbers less that whose digit adds up to 7. Hence the answer is

*Key Idea: Bijection; Number of Non Negative Integer Solutions to an equation*

*Related*

But we cannot have the first digit to be zero. So, x_1>0.

Therefore we should reserve at least 1 value to x_1.

Therefore x_1+x_2+x_3+……+x_8=6 then all the non negative solutions should be accepted.

Since 1 has already been assigned to x_1.