Melody

If you want help with knowing where you went wrong then you should post what you have tried to do yourself and ask specific questions.

Also, if it is a direct AOPS question you should not post it here. Especially not in its entirity.

Could you please give us a link to the original question so that I can link the 2 together. Thanks ItsFree

Here is the pic.

Check it is right then try to answer from there.

Ask questions if you want.

You ask specific questions and learn from the answers.

To start with if you are adding you can think of  a number inside a square root as like a letter

For example.

Hopefull you know that    $x+y$ can not be simplified

In the same way       $\sqrt2+\sqrt3$       cannot be simplified.

But hopfully you also know that      $1x+5x+y=6x+y$

Likewise          $1\sqrt2+5\sqrt2+\sqrt3=6\sqrt2+\sqrt3$

I guess that means you were only interested in the answer? 

I think AX is meant to be PX ? 

Please proofread your question.

ok now I understand what you have done.

In this case order does not count.  I am glad you worked that out for yourself :)

This is how I would look at it.

Choose 2 dogs from  12 long haired ones   and    Choose 3 cats from ll long haireds ones 

and put it over  5 animals from a total of 30 animals

= ( 12C2 * 11C3 ) / 30C5    =   66*165 / 142506  =  10890 / 142506 = 605 / 7917   = approx 7.6%

That sounds ok to me.

I do not know why you multiplied that by 5C2

79pi     m^2

hint:

      (x+8) * x  =  884