If \(\alpha_n\) is the coefficient of \(x^n\) in the expansion of \((1-x)^{-5}\) and \(\beta_n\) is the coefficient of \(x^n\) in the expansion of \((1-x)^{-4}\), then \(\alpha_{12} + \beta_{13}\) is equal to:
Show Hint
The coefficient of \(x^n\) in \((1-x)^{-r}\) is
\[
{}^{n+r-1}C_{r-1}.
\]
After obtaining coefficients, look for Pascal's identity to simplify expressions involving sums of combinations.