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Can someone please tell me whether I can use negative binomial distribution for this question.

"If there are 3 types of books in a bookstore and each book has an equal probability of being bought. What is the expected number of purchases to get all 3 books?"

Using negative negative binomial, i get E(Y)=3/(1/3)=9. Is it just supposed to be this or is there something else to a question like this?

Any help would be great.

Thank you in advance.