  Stirling approximation of the factorials and multinominal coefficients are
generalized based on the one-parameter ($\kappa$) deformed functions introduced
by Kaniadakis [Phys. Rev. E \textbf{66} (2002) 056125]. We have obtained the
relation between the $\kappa$-generalized multinominal coefficients and the
$\kappa$-entropy by introducing a new $\kappa$-product operation.
