probability

So, any red toy is desirable, as is any large toy.
My take..

There are 4 possible large toys (1 of each color) and 3 possible red toys (1 of each size). Here's where we have to be careful: we've counted the large red toy in both groups, so the total # of desired outcomes is 7-1=6, out of 12 total possible toys, to give us an answer of:

6/12 = 1/2

The question is confusing, but the driving point is: what is the probability that at least one of the color and model will satisfy the boy?

Checking via the long method yields the following:

yellow small
yellow middle
yellow large
blue small
blue middle
blue large
green small
green middle
green large
red small
red middle
red large

So there are 12 possibilities.

Now if we list the ones that have AT LEAST ONE of the qualities "red" or "large", we have:


yellow large
blue large
green large
red small
red middle
red large

so that leaves 6 possible outcomes.

So the final answer is 6/12 = 1/2

three sizes- large,medium and small

Hamm0 is right, total no. of toys is 4 x 3. i was wrong to calculate it as 4! x 3!