Combining the Spins of 3 spin 1 particles

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Homework Statement
Find the normalized spin states for three identical non-interacting bosons where two have m_s = 1, and one has m_s = 0
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I am having trouble with the normalization part.
To get a spin ##|32>## state I could have the following possibilities
##C_1|111110> + C_2|111011> + C_3|101111>##

This should be equivalent to
##C_1|11>|21> + C_2|11>|21> + C_3|10>|22>##
That is a spin 1 particle and a spin 2 particle that need to be combined.
So, to get the normalization coefficients would I just look these up in the Clepsch Gordon Table and that's all?
 
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I would be careful here. If you add three spins ##S=1## with ##M_S=2##, is ##| 32\rangle## the only possibility?
 
Thanks, I see what the problem is, also I was using bad representation of the spins, this is from chapter 7 problem 7 in Sakurai 2nd ed. and the way my professor told me to do the problem made it a lot easier.
 
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