Feller's two volume classic [1] has plenty of motivation - his exposition of combinatorics at the beginning of the first volume is a great introduction to that

Feller's two volume classic [1] has plenty of motivation - his exposition of combinatorics at the beginning of the first volume is a great introduction to that subject! However, it wasn't written with algorithms in mind. Venkatesh's more recent volume [2] is very well motivated and is better suited to modern engineering applications. Both have lots of exercises. [1] https://www.amazon.com/Introduction-Probability-Theory-Applications-Vol/dp/0471257087 https://www.amazon.com/Introduction-Probability-Theory-Appli... [2] https://www.amazon.com/Theory-Probability-Explorations-Applications/dp/1107024471 https://www.amazon.com/Theory-Probability-Explorations-Appli...