John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work? Choose one.
A) 1/2	B) 2/5	C) 3/10	D) 7/20	E) 8/45
For the denominator, we are going to pick two books from among ten total: a combination of two from ten. Again, we will use the formula:   nC2 = n(n-1)/2   which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers. Here   10C2=10(9)/2=5*9= 
<gadget id="calculator">5*9</gadget>
<output>45</output>
45   That’s the total number of pairs of books we could pick from the ten on the shelf. That’s our denominator.   Now, the numerator. We want one novel and one reference work. Well, there are four novels and two reference works, so by the FCP, the number of ways we can pick this is 4 x 2= 8. That’s the total possible number of pairs involving exactly one of these four novels and exactly one of these two reference works. That’s our numerator.   probability= 8/45   Answer = 8/45
<result>E</result>
John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?