Combinatorics and Probability mix-Hard

[dddanny2006]

A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 90 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90 ). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
(A) 3/16000
(B) 1/8100
(C) 3/1600
(D) 1/90
(E) 2/45

We have 90Cellos in the 800Cellos that can partner 90Violas in the 600Violas(Each one has its own wood partner)

Probability of choosing two at random such that both were made of the wood from same tree is

Cellos--P(Choosing Cellos among 90Cellos in 800)
= (90/800)

Violas
=(90/600)

(90/800)*(90/600)
=0.016875
=27/1600

The answer doesnt feature among the options.

Source=Veritas

[RonPurewal]

Hi,
As I mentioned here --
post94482.html#p94482
-- we can't continue to answer posts with titles that don't conform to the forum rules.

Please read the forum rules -- first thread in every folder -- and then re-post your question with an appropriate title (i.e., based on the first few words of the question).

Thanks.