All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number \( n \) be denoted by \( W_{n} \). Let the probability \( P(W_{n}) \) of choosing the word \( W_{n} \) satisfy \( P(W_{n}) = 2P(W_{n-1}), \ n > 1 \). If \( P(CDBEA) = \frac{2^{\alpha}}{2^{\beta} - 1}, \ \alpha, \beta \in \)\(\mathbb{N}\), then \( \alpha + \beta \) is equal to _________.
