ardz24 wrote: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?

(A) 1/2
(B) 2/5
(C) 3/10
(D) 7/20
(E) 8/45

OA: E
I'm confused how to set up the formulas here. Can any experts help?

There are a total of 10 books: 4 Poetry; 4 Novels; and 2 Reference

Ways of picking up any 2 books = 10C2 = 10.9/1.2 = 45
Ways of picking up any 1 Poetry and 1 Reference books = 4C1 * 2C1 = 8

The probability that we pick one novel and one reference work = 8/45

The correct answer: E

Hope this helps!

-Jay
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Hi ardz24,

We're told that John has on his shelf 4 books of poetry, 4 novels, and 2 reference works. We're asked to pick two books at random and we're asked for the probability that we pick one novel and one reference work. This question can be solved in a couple of different ways. Here's how you can solve it with Permutations:

There are two different ways to end up with 1 novel and 1 reference work (depending on which one you pick first):

(novel 1st)(reference 2nd) = (4/10)(2/9) = 8/90
(reference 1st)(novel 2nd) = (2/10)(4/9) = 8/90
Total ways to get 1 novel and 1 reference work = (8/90) + (8/90) = 16/90 = 8/45

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorAT wrote: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?

(A) 1/2
(B) 2/5
(C) 3/10
(D) 7/20
(E) 8/45

OA: E
I'm confused how to set up the formulas here. Can any experts help?

The probability of picking one novel and one reference work is:

P(novel followed by reference work) = 4/10 x 2/9 = 4/45

or

P(reference work followed by novel) =2/10 x 4/9 = 4/45

So, the overall probability is 4/45 + 4/45 = 8/45.

Answer: E