Adding Spin S1 and S2: A Puzzling Situation

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I am reading the section in Griffiths' Quantum about adding spins together. It says if you have a particle of spin s1 and another of spin s2 then the possible composite spins are

s1+s2, s1+s2 -1, s1+s2-2, ... |s1-s2|

that rule (though not proven in this text) has seemed straight forward to me until now. I have a particle of spin 1/2 and a particle of spin 3/2, so I get

5/2, 3/2 ... but then the situation of them aligning antiparallel 3/2-1/2 = 1 does not occur as one of the integer steps, so do I include it as a possibility? It seems strange that the anti parallel arrangement should not be a possibility.

Thanks for the help

UPDATE:

3/2+1/2 = 2 not 2.5

One day I will figure out how to add those fractions together
 
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dsr39 said:
I have a particle of spin 1/2 and a particle of spin 3/2, so I get

5/2, 3/2 ...

How?
 
That is a very good question. Thank you
 
Am I banned for asking that? I understand if so
 
We all make these obvious mistakes sometimes. Don't worry about it. ;)
 

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