Bird Question: selecting finches from covered cage

[zebrafinch]

A covered cage contains 12 zebra finches, 8 society finches, and 6 owl finches. If two finches are randomly selected at the same time, what is the probability that they match?

I assume that it depends on which kind of bird is pulled out first?

I think the probability of pulling out the first finch would be----Zebra (12/26) Society (8/26) Owl(6/26)

If you pull out say a Zebra on the first grab, then the second would be (12/26)(11/25)2 ?????????????

Im not sure if I am doing this right?

 

[galactus]

You're thinking on the right lines.

\(\displaystyle (12/26)(11/25)+(8/26)(7/25)+(6/26)(5/25)\)

or

\(\displaystyle \frac{C(12,2)+C(8,2)+C(6,2)}{C(26,2)}\)

 

[Denis]

That problem is for the birds :roll: