There are 10 books on a shelf: 5 English books, 5 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?  Pick:
A) 1
B) 0
C) 1/3
D) 31/45
E) 28/90
Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)   METHOD-1   Favourable Outcomes   Case-1: One book is English (out of 5 English books) and one book is Spanish (out of 5 Spanish books) i.e. 5C1*5C1   Case-2: One book is Spanish (out of 5 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 5C1*2C1   Case-3: One book is English (out of 5 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 5C1*2C1   Total favourable Outcomes = 5C1*5C1+5C1*2C1+5C1*2C1 = 25+10+10= 
<gadget id="calculator">25+10+10</gadget>
<output>45</output>
45   Total Possible Outcomes= 10C2 = 45   i.e. Probability = 45/45= 
<gadget id="calculator">45/45</gadget>
<output>1</output>
1   1
<result>A</result>
There are 10 books on a shelf: 5 English books, 5 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?