A certain music store stocks 800 cellos and 600 violas

[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]

Think about the situation with each choice you're making here.

In your approach, you're choosing a cello first. That part of the solution is fine: there are 90 "eligible" cellos, so that's 90 out of 800.

The issue is the other fraction. At this point, you've already chosen one particular cello, so you don't just want any random one of those 90 violas. You only want the one specific viola that actually corresponds to the cello you've already picked.

So, the second fraction should be 1/600, not 90/600.

Incidentally, this problem is basically identical to #217 in the 11th edition official guide.