Discovering the Total Number of States and How It Was Noted

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How did they "note" this from (16)?

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110122_121814.jpg?t=1295721126
 
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It's probably more straightforward to use the formula for g(s,N) in (15) and note that it's just the binomial coefficient.
 
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