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-Appli...

[2] https://www.amazon.com/Theory-Probability-Explorations-Appli...