Book on discrete mathematics for self study

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I am searching for book on discrete mathematics which is suitable for self study. This mean I want it to have exercises with answers (It would be ideal if it had solutions). I have already read "Discrete Mathematics" of Kenneth Ross. I have also partially read "Concrete Mathematics" of Knuth but I didn't like the style much. I am searching for next book to read. I do not have any requirements on topics I just want it to cover few of them like combinatorics and counting, recurrences and probably generating functions.

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I'm taking a Discrete Mathematics course right now, using Applied combinatorics by Roberts and Tesman. It does have some good 'real life' examples and applications.