What is the probability of getting the sum $26$ when $7$ chips are taken out? Suppose you have a bag in which there are $10$ chips numbered $0$ to $9$. You take out a chip at random, note its number and then put it back. This process is done $7$ times and after that the numbers are added. 

What is the probability that the sum is $26$?

The probability of getting any number at any turn is $\frac1{10}$.  Also I know that there are $10^7$ different combinations that can be formed from these numbers. But it would be too inefficient to start counting which ones sum up to $26$. 
I have really no idea what to do. Can this be done in a faster way using combinatorics? If yes, how?

The number of ways of drawing 7 chits with sum equal to 26 is the coefficient of $x^{26}$ in the expansion
\begin{align*}
(1+x+x^2+\cdots +x^9)^7 &= \left(\frac{1-x^{10}}{1-x}\right)^7 \\
&=(1-7x^{10} + 21x^{20} - \cdots)\left(1+\binom{7}{1}x + \binom{8}{2}x^2 + \cdots\right)
\end{align*}
Coefficient of $x^{26}$ is
$$\binom{32}{26} - 7\cdot \binom{22}{16} + 21\cdot \binom{12}{6} = 403305$$
