Nothing
8*5*4 / choose(17,3) # 1 sock of each kind means no pairs
1 - (8*5*4 / choose(17,3)) # so this is prob of getting a pair
# or do it this way
( choose(8,2)*9 + choose(5,2) * 12 + choose(4,2) * 13 +
choose(8,3) + choose(5,3) + choose(4,3) ) / choose(17,3)
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