Mr. Robson is teaching a primer on Algebraic Geometry to his pigs and chicken. He has seven animals in his advanced maths class. Unfortunately, he cannot remember which animals go with which names. He has just produced their first set of reports and needs to give it back to them. He decides to just guess!

He can identify whether or not a report belongs to a pig or a chicken, as pig's name always begin with P and chicken's names always begin with C, and so will definitely give a pig's work to a pig and a chicken's work to a chicken.

Each report either says "you do excellent work, continue" or "you do poor, you should improve", and it's important that an animal gets a report that says the right comment. Two of the pigs and two of the chickens have recieved excellent work There are 4 chickens and 3 pigs in the class.

What is the chance that every animal gets an appropriate report?

 

And then, generalise your result!