There are 10 books on a shelf: 5 English books, 4 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?	Choose the correct choice from the following options.
A) 31/90	B) 3/10	C) 1/3	D) 38/45	E) 28/90
Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)   Favourable Outcomes   Case-1: One book is English (out of 5 English books) and one book is Spanish (out of 4 Spanish books) i.e. 5C1*4C1   Case-2: One book is Spanish (out of 4 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 4C1*2C1   Case-3: One book is English (out of 8 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 8C1*2C1   Total favourable Outcomes = 5C1*4C1+4C1*2C1+5C1*2C1 = 20+8+10= 
<gadget id="calculator">20+8+10</gadget>
<output>38</output>
38   Total Possible Outcomes= 10C2 = 45   i.e. Probability = 38/45   38/45
<result>D</result>
There are 10 books on a shelf: 5 English books, 4 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?