Break the problem into a series of events — pulling the first book, then the second book. The probability of choosing 2 books in different language then depends on the language of the first book:

1) picking an English book AND picking a not-English book

2) picking an Spanish book AND picking a not-Spanish book

3) picking a Portuguese book AND picking a not-Portuguese book

In questions that present several scenarios, or several ways (which may consist of a series of events) of reaching the desired result:

A) Calculate the probability of each scenario separately.

B) Since the scenarios are different ways of reaching the same result with an OR relationship between them, ADD the probabilities.

1) There are 5 English books out of 10 total books, so the odds of picking an English book are 5/10. There are 5 books not in English, so the odds of pulling a second book not in English are 5/9 (only 9 books in total, because one is already out after the first pick). So the probability of this scenario is:

--> 5/10 × 5/9 = 25/90

2) There are 3 Spanish books out of 10 total books, so the odds of picking a Spanish book are 3/10. There are 7 books not in Spanish, so the odds of pulling a second book not in Spanish are 7/9 (only 9 books in total, because one is already out after the first pick). So the probability of this scenario is:

--> 3/10 × 7/9 = 21/90

3) There are 2 Portuguese books out of 10 total books, so the odds of picking a Portuguese book are 2/10. There are 8 books not in Portuguese , so the odds of pulling a second book not in Portuguese are 8/9 (only 9 books in total, because one is already out after the first pick). So the probability of this scenario is:

--> 2/10 × 8/9 = 16/90

Since there's an "OR" relationship between scenarios, add them to get the total probability:

--> 25/90 + 21/90 + 16/90 = 62/90 = 31/45