There are 10 books on a shelf: 4 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?
Answers
A) 31/90	B) 3/10	C) 1/3	D) 4/7	E) 28/90
Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)   Favourable Outcomes   Case-1: One book is English (out of 4 English books) and one book is Spanish (out of 3 Spanish books) i.e. 4C1*3C1   Case-2: One book is Spanish (out of 3 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 3C1*2C1   Case-3: One book is English (out of 4 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 4C1*2C1   Total favourable Outcomes = 4C1*3C1+3C1*2C1+4C1*2C1 = 12+6+8= 
<gadget id="calculator">12+6+8</gadget>
<output>26</output>
26   Total Possible Outcomes= 10C2 = 45   i.e. Probability = 26/45 = 4/7   4/7
<result>D</result>
There are 10 books on a shelf: 4 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?