Assume that there are 6 rats in the cage...

Question

Assume that there are 6 rats in the cage: 4 trained and 2 untrained. A rat is removed from the cage and it is noted whether or not it is trained. It is then placed in a different cage. 4 more rats are removed and treated the same way. How many outcomes are possible for this experiment?

Answer 1

If we consider the rats unique (maybe they are wearing tiny name tags) then since 5 rats are being selected it can happen in ₆C_{5 ways.}

 

If you are only recording T (trained) and U (untrained) then you will have e.g. TTTTU or TTTUU plus all rearrangements of these two possibilities.

 

Calculate all rearrangements of TTTTU and then rearrangements of TTTUU and add (because they are mutually exclusive.)

 

 

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