Word Probability Calculation (Jee Mains)

Classical and Conditional Probability

Hard

Word Probability Calculation

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) = $\frac{{{2^\alpha }}}{{{2^\beta } - 1}},\alpha ,\beta \in {\Bbb N}$ then α + β is equal to : ______

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