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…

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 $\displaystyle n$ be denoted by $\displaystyle \mathrm{W}_{\mathrm{n}}$. Let the probability $\displaystyle \mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)$ of choosing the word $\displaystyle \mathrm{W}_{\mathrm{n}}$ satisfy $\displaystyle \mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)=2 \mathrm{P}\left(\mathrm{W}_{\mathrm{n}-1}\right), \mathrm{n}>1$. If $\displaystyle \mathrm{P}(\mathrm{CDBEA})=\frac{2^\alpha}{2^\beta-1}, \alpha, \beta \in \mathbb{N}$, then $\displaystyle \alpha+\beta$ is equal to : $\displaystyle \_\_\_\_$