This is a problem from a brazilian probability book called "Probabilidade e Variáveis Aleatórias" (Probability and Random Variables) [MAGALHAES, M. N. 2015]:
"Cards are drawn without replacement from a deck of 52 cards until all four aces are chosen. Find the expectation of the number of draws using conditioning."
I've tried some approaches explained in other related questions/answers (Hypergeometric Distribution, Negative Hypergeometric) but I didn't manage to do that using conditioning. The correct answer is supposed to be 52 according the book. I don't know whether it makes sense, considering the results shown in similar questions.
I'm thinking about the property $E(X) = E(E(X|Y))$ but I'm not making any progress.
I would appreciate any help.